LMFDB - Embedded newform 1050.2.bc.g.157.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1050,2,Mod(157,1050)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1050, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 2]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1050.157");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1050.bc (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$8.38429221223$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{12})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} + 12 x^{14} - 48 x^{13} + 67 x^{12} - 24 x^{11} + 118 x^{10} - 176 x^{9} + 351 x^{8} + \cdots + 4 $ x^16 - 4x^15 + 12x^14 - 48x^13 + 67x^12 - 24x^11 + 118x^10 - 176x^9 + 351x^8 - 180x^7 + 358x^6 - 336x^5 + 390x^4 - 344x^3 + 164x^2 - 40*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 210)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			157.4
Root			$0.792206 - 1.03242i$ of defining polynomial
Character	$\chi$	$=$	1050.157
Dual form			1050.2.bc.g.943.4

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.258819 - 0.965926i) q^{2} +(-0.965926 + 0.258819i) q^{3} +(-0.866025 - 0.500000i) q^{4} +1.00000i q^{6} +(1.52856 - 2.15951i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(0.866025 - 0.500000i) q^{9} +O(q^{10})$	\(q+(0.258819 - 0.965926i) q^{2} +(-0.965926 + 0.258819i) q^{3} +(-0.866025 - 0.500000i) q^{4} +1.00000i q^{6} +(1.52856 - 2.15951i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(0.866025 - 0.500000i) q^{9} +(0.883028 - 1.52945i) q^{11} +(0.965926 + 0.258819i) q^{12} +(-2.71395 - 2.71395i) q^{13} +(-1.69031 - 2.03540i) q^{14} +(0.500000 + 0.866025i) q^{16} +(0.574830 + 2.14529i) q^{17} +(-0.258819 - 0.965926i) q^{18} +(0.886994 + 1.53632i) q^{19} +(-0.917556 + 2.48155i) q^{21} +(-1.24879 - 1.24879i) q^{22} +(3.90900 + 1.04741i) q^{23} +(0.500000 - 0.866025i) q^{24} +(-3.32389 + 1.91905i) q^{26} +(-0.707107 + 0.707107i) q^{27} +(-2.40353 + 1.10591i) q^{28} -3.84628i q^{29} +(-8.94554 - 5.16471i) q^{31} +(0.965926 - 0.258819i) q^{32} +(-0.457089 + 1.70588i) q^{33} +2.22097 q^{34} -1.00000 q^{36} +(0.861499 - 3.21516i) q^{37} +(1.71354 - 0.459142i) q^{38} +(3.32389 + 1.91905i) q^{39} -11.8993i q^{41} +(2.15951 + 1.52856i) q^{42} +(-3.46335 + 3.46335i) q^{43} +(-1.52945 + 0.883028i) q^{44} +(2.02344 - 3.50471i) q^{46} +(-5.93837 - 1.59118i) q^{47} +(-0.707107 - 0.707107i) q^{48} +(-2.32699 - 6.60190i) q^{49} +(-1.11049 - 1.92342i) q^{51} +(0.993373 + 3.70732i) q^{52} +(-0.106258 - 0.396561i) q^{53} +(0.500000 + 0.866025i) q^{54} +(0.446149 + 2.60786i) q^{56} +(-1.25440 - 1.25440i) q^{57} +(-3.71522 - 0.995491i) q^{58} +(5.18379 - 8.97859i) q^{59} +(-5.87936 + 3.39445i) q^{61} +(-7.30401 + 7.30401i) q^{62} +(0.244018 - 2.63447i) q^{63} -1.00000i q^{64} +(1.52945 + 0.883028i) q^{66} +(7.37834 - 1.97702i) q^{67} +(0.574830 - 2.14529i) q^{68} -4.04689 q^{69} -10.7193 q^{71} +(-0.258819 + 0.965926i) q^{72} +(-10.2705 + 2.75198i) q^{73} +(-2.88263 - 1.66429i) q^{74} -1.77399i q^{76} +(-1.95310 - 4.24477i) q^{77} +(2.71395 - 2.71395i) q^{78} +(-10.9907 + 6.34546i) q^{79} +(0.500000 - 0.866025i) q^{81} +(-11.4939 - 3.07978i) q^{82} +(1.94227 + 1.94227i) q^{83} +(2.03540 - 1.69031i) q^{84} +(2.44896 + 4.24172i) q^{86} +(0.995491 + 3.71522i) q^{87} +(0.457089 + 1.70588i) q^{88} +(-0.558127 - 0.966705i) q^{89} +(-10.0092 + 1.71236i) q^{91} +(-2.86158 - 2.86158i) q^{92} +(9.97746 + 2.67345i) q^{93} +(-3.07393 + 5.32419i) q^{94} +(-0.866025 + 0.500000i) q^{96} +(7.26720 - 7.26720i) q^{97} +(-6.97922 + 0.539001i) q^{98} -1.76606i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{7}+O(q^{10}) $ 16 * q + 4 * q^7	$ 16 q + 4 q^{7} + 4 q^{11} - 16 q^{13} - 16 q^{14} + 8 q^{16} - 12 q^{17} + 8 q^{19} + 8 q^{21} - 4 q^{22} + 40 q^{23} + 8 q^{24} - 12 q^{26} + 4 q^{28} - 24 q^{31} - 4 q^{33} - 16 q^{34} - 16 q^{36} + 8 q^{37} + 20 q^{38} + 12 q^{39} - 8 q^{42} + 24 q^{43} - 4 q^{46} - 52 q^{49} + 8 q^{51} - 8 q^{52} + 28 q^{53} + 8 q^{54} + 8 q^{56} + 8 q^{57} + 12 q^{58} - 8 q^{59} + 24 q^{61} + 8 q^{62} + 4 q^{63} + 84 q^{67} - 12 q^{68} + 8 q^{69} - 32 q^{71} - 16 q^{73} + 24 q^{74} - 44 q^{77} + 16 q^{78} - 12 q^{79} + 8 q^{81} - 36 q^{82} - 16 q^{83} - 4 q^{84} - 8 q^{86} - 48 q^{87} + 4 q^{88} + 16 q^{89} + 8 q^{91} - 8 q^{92} + 32 q^{93} - 8 q^{94} + 44 q^{97} - 24 q^{98}+O(q^{100}) $ 16 * q + 4 * q^7 + 4 * q^11 - 16 * q^13 - 16 * q^14 + 8 * q^16 - 12 * q^17 + 8 * q^19 + 8 * q^21 - 4 * q^22 + 40 * q^23 + 8 * q^24 - 12 * q^26 + 4 * q^28 - 24 * q^31 - 4 * q^33 - 16 * q^34 - 16 * q^36 + 8 * q^37 + 20 * q^38 + 12 * q^39 - 8 * q^42 + 24 * q^43 - 4 * q^46 - 52 * q^49 + 8 * q^51 - 8 * q^52 + 28 * q^53 + 8 * q^54 + 8 * q^56 + 8 * q^57 + 12 * q^58 - 8 * q^59 + 24 * q^61 + 8 * q^62 + 4 * q^63 + 84 * q^67 - 12 * q^68 + 8 * q^69 - 32 * q^71 - 16 * q^73 + 24 * q^74 - 44 * q^77 + 16 * q^78 - 12 * q^79 + 8 * q^81 - 36 * q^82 - 16 * q^83 - 4 * q^84 - 8 * q^86 - 48 * q^87 + 4 * q^88 + 16 * q^89 + 8 * q^91 - 8 * q^92 + 32 * q^93 - 8 * q^94 + 44 * q^97 - 24 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times$.

$n$	$127$	$451$	$701$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{1}{6}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.258819	−	0.965926i	0.183013	−	0.683013i
$2$	0.258819	−	0.965926i	0.183013	−	0.683013i
$3$	−0.965926	+	0.258819i	−0.557678	+	0.149429i
$3$	−0.965926	+	0.258819i	−0.557678	+	0.149429i
$4$	−0.866025	−	0.500000i	−0.433013	−	0.250000i
$5$		0			0
$5$		0			0
$6$			1.00000i			0.408248i
$7$	1.52856	−	2.15951i	0.577743	−	0.816219i
$7$	1.52856	−	2.15951i	0.577743	−	0.816219i
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$	0.866025	−	0.500000i	0.288675	−	0.166667i
$10$		0			0
$11$	0.883028	−	1.52945i	0.266243	−	0.461147i	−0.701645	−	0.712526i	$-0.747551\pi$
$11$	0.883028	−	1.52945i	0.266243	−	0.461147i	0.967889	+	0.251380i	$0.0808843\pi$
$12$	0.965926	+	0.258819i	0.278839	+	0.0747146i
$13$	−2.71395	−	2.71395i	−0.752713	−	0.752713i	0.222272	−	0.974985i	$-0.428653\pi$
$13$	−2.71395	−	2.71395i	−0.752713	−	0.752713i	−0.974985	+	0.222272i	$0.928653\pi$
$14$	−1.69031	−	2.03540i	−0.451754	−	0.543984i
$15$		0			0
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	0.574830	+	2.14529i	0.139417	+	0.520310i	0.999941	+	0.0109000i	$0.00346965\pi$
$17$	0.574830	+	2.14529i	0.139417	+	0.520310i	−0.860524	+	0.509410i	$0.829864\pi$
$18$	−0.258819	−	0.965926i	−0.0610042	−	0.227671i
$19$	0.886994	+	1.53632i	0.203490	+	0.352456i	0.949651	−	0.313311i	$-0.101438\pi$
$19$	0.886994	+	1.53632i	0.203490	+	0.352456i	−0.746160	+	0.665766i	$0.768105\pi$
$20$		0			0
$21$	−0.917556	+	2.48155i	−0.200227	+	0.541519i
$22$	−1.24879	−	1.24879i	−0.266243	−	0.266243i
$23$	3.90900	+	1.04741i	0.815082	+	0.218401i	0.642195	−	0.766541i	$-0.278024\pi$
$23$	3.90900	+	1.04741i	0.815082	+	0.218401i	0.172887	+	0.984942i	$0.444691\pi$
$24$	0.500000	−	0.866025i	0.102062	−	0.176777i
$25$		0			0
$26$	−3.32389	+	1.91905i	−0.651869	+	0.376356i
$27$	−0.707107	+	0.707107i	−0.136083	+	0.136083i
$28$	−2.40353	+	1.10591i	−0.454225	+	0.208998i
$29$		−	3.84628i		−	0.714236i	−0.934059	−	0.357118i	$-0.883759\pi$
$29$		−	3.84628i		−	0.714236i	0.934059	−	0.357118i	$-0.116241\pi$
$30$		0			0
$31$	−8.94554	−	5.16471i	−1.60667	−	0.927610i	−0.990109	−	0.140300i	$-0.955193\pi$
$31$	−8.94554	−	5.16471i	−1.60667	−	0.927610i	−0.616558	−	0.787310i	$-0.711473\pi$
$32$	0.965926	−	0.258819i	0.170753	−	0.0457532i
$33$	−0.457089	+	1.70588i	−0.0795690	+	0.296956i
$34$	2.22097			0.380893
$35$		0			0
$36$	−1.00000			−0.166667
$37$	0.861499	−	3.21516i	0.141630	−	0.528569i	−0.858253	−	0.513227i	$-0.828450\pi$
$37$	0.861499	−	3.21516i	0.141630	−	0.528569i	0.999882	−	0.0153416i	$-0.00488357\pi$
$38$	1.71354	−	0.459142i	0.277973	−	0.0744827i
$39$	3.32389	+	1.91905i	0.532248	+	0.307294i
$40$		0			0
$41$		−	11.8993i		−	1.85836i	−0.369622	−	0.929182i	$-0.620513\pi$
$41$		−	11.8993i		−	1.85836i	0.369622	−	0.929182i	$-0.379487\pi$
$42$	2.15951	+	1.52856i	0.333220	+	0.235862i
$43$	−3.46335	+	3.46335i	−0.528155	+	0.528155i	−0.920022	−	0.391867i	$-0.871829\pi$
$43$	−3.46335	+	3.46335i	−0.528155	+	0.528155i	0.391867	+	0.920022i	$0.371829\pi$
$44$	−1.52945	+	0.883028i	−0.230573	+	0.133122i
$45$		0			0
$46$	2.02344	−	3.50471i	0.298341	−	0.516741i
$47$	−5.93837	−	1.59118i	−0.866200	−	0.232098i	−0.201756	−	0.979436i	$-0.564665\pi$
$47$	−5.93837	−	1.59118i	−0.866200	−	0.232098i	−0.664444	+	0.747338i	$0.731332\pi$
$48$	−0.707107	−	0.707107i	−0.102062	−	0.102062i
$49$	−2.32699	−	6.60190i	−0.332427	−	0.943129i
$50$		0			0
$51$	−1.11049	−	1.92342i	−0.155499	−	0.269332i
$52$	0.993373	+	3.70732i	0.137756	+	0.514113i
$53$	−0.106258	−	0.396561i	−0.0145957	−	0.0544719i	0.958244	−	0.285952i	$-0.0923098\pi$
$53$	−0.106258	−	0.396561i	−0.0145957	−	0.0544719i	−0.972840	+	0.231480i	$0.925643\pi$
$54$	0.500000	+	0.866025i	0.0680414	+	0.117851i
$55$		0			0
$56$	0.446149	+	2.60786i	0.0596191	+	0.348490i
$57$	−1.25440	−	1.25440i	−0.166149	−	0.166149i
$58$	−3.71522	−	0.995491i	−0.487833	−	0.130714i
$59$	5.18379	−	8.97859i	0.674872	−	1.16891i	−0.301634	−	0.953424i	$-0.597532\pi$
$59$	5.18379	−	8.97859i	0.674872	−	1.16891i	0.976506	−	0.215489i	$-0.0691346\pi$
$60$		0			0
$61$	−5.87936	+	3.39445i	−0.752775	+	0.434615i	−0.826696	−	0.562649i	$-0.809782\pi$
$61$	−5.87936	+	3.39445i	−0.752775	+	0.434615i	0.0739204	+	0.997264i	$0.476449\pi$
$62$	−7.30401	+	7.30401i	−0.927610	+	0.927610i
$63$	0.244018	−	2.63447i	0.0307434	−	0.331913i
$64$		−	1.00000i		−	0.125000i
$65$		0			0
$66$	1.52945	+	0.883028i	0.188262	+	0.108693i
$67$	7.37834	−	1.97702i	0.901408	−	0.241532i	0.221787	−	0.975095i	$-0.428811\pi$
$67$	7.37834	−	1.97702i	0.901408	−	0.241532i	0.679621	+	0.733563i	$0.262144\pi$
$68$	0.574830	−	2.14529i	0.0697083	−	0.260155i
$69$	−4.04689			−0.487188
$70$		0			0
$71$	−10.7193			−1.27214			−0.636072	−	0.771629i	$-0.719442\pi$
$71$	−10.7193			−1.27214			−0.636072	+	0.771629i	$0.719442\pi$
$72$	−0.258819	+	0.965926i	−0.0305021	+	0.113835i
$73$	−10.2705	+	2.75198i	−1.20207	+	0.322095i	−0.803647	−	0.595106i	$-0.797110\pi$
$73$	−10.2705	+	2.75198i	−1.20207	+	0.322095i	−0.398426	+	0.917200i	$0.630444\pi$
$74$	−2.88263	−	1.66429i	−0.335099	−	0.193470i
$75$		0			0
$76$		−	1.77399i		−	0.203490i
$77$	−1.95310	−	4.24477i	−0.222577	−	0.483737i
$78$	2.71395	−	2.71395i	0.307294	−	0.307294i
$79$	−10.9907	+	6.34546i	−1.23655	+	0.713920i	−0.968386	−	0.249455i	$-0.919749\pi$
$79$	−10.9907	+	6.34546i	−1.23655	+	0.713920i	−0.268159	+	0.963375i	$0.586415\pi$
$80$		0			0
$81$	0.500000	−	0.866025i	0.0555556	−	0.0962250i
$82$	−11.4939	−	3.07978i	−1.26929	−	0.340104i
$83$	1.94227	+	1.94227i	0.213191	+	0.213191i	0.805622	−	0.592430i	$-0.201831\pi$
$83$	1.94227	+	1.94227i	0.213191	+	0.213191i	−0.592430	+	0.805622i	$0.701831\pi$
$84$	2.03540	−	1.69031i	0.222081	−	0.184428i
$85$		0			0
$86$	2.44896	+	4.24172i	0.264078	+	0.457396i
$87$	0.995491	+	3.71522i	0.106728	+	0.398314i
$88$	0.457089	+	1.70588i	0.0487259	+	0.181847i
$89$	−0.558127	−	0.966705i	−0.0591614	−	0.102471i	0.834928	−	0.550359i	$-0.185509\pi$
$89$	−0.558127	−	0.966705i	−0.0591614	−	0.102471i	−0.894089	+	0.447889i	$0.852176\pi$
$90$		0			0
$91$	−10.0092	+	1.71236i	−1.04925	+	0.179504i
$92$	−2.86158	−	2.86158i	−0.298341	−	0.298341i
$93$	9.97746	+	2.67345i	1.03461	+	0.277224i
$94$	−3.07393	+	5.32419i	−0.317051	+	0.549149i
$95$		0			0
$96$	−0.866025	+	0.500000i	−0.0883883	+	0.0510310i
$97$	7.26720	−	7.26720i	0.737872	−	0.737872i	−0.234293	−	0.972166i	$-0.575278\pi$
$97$	7.26720	−	7.26720i	0.737872	−	0.737872i	0.972166	+	0.234293i	$0.0752777\pi$
$98$	−6.97922	+	0.539001i	−0.705007	+	0.0544473i
$99$		−	1.76606i		−	0.177495i
$100$		0			0
$101$	15.8887	+	9.17333i	1.58098	+	0.912780i	0.994716	+	0.102661i	$0.0327358\pi$
$101$	15.8887	+	9.17333i	1.58098	+	0.912780i	0.586265	+	0.810119i	$0.300598\pi$
$102$	−2.14529	+	0.574830i	−0.212416	+	0.0569166i
$103$	−2.36040	+	8.80911i	−0.232577	+	0.867988i	0.746650	+	0.665217i	$0.231661\pi$
$103$	−2.36040	+	8.80911i	−0.232577	+	0.867988i	−0.979226	+	0.202770i	$0.935006\pi$
$104$	3.83810			0.376356
$105$		0			0
$106$	−0.410550			−0.0398762
$107$	3.81880	−	14.2519i	0.369177	−	1.37779i	−0.492492	−	0.870317i	$-0.663914\pi$
$107$	3.81880	−	14.2519i	0.369177	−	1.37779i	0.861669	−	0.507471i	$-0.169419\pi$
$108$	0.965926	−	0.258819i	0.0929463	−	0.0249049i
$109$	17.4494	+	10.0744i	1.67135	+	0.964955i	0.966883	+	0.255218i	$0.0821474\pi$
$109$	17.4494	+	10.0744i	1.67135	+	0.964955i	0.704467	+	0.709736i	$0.251186\pi$
$110$		0			0
$111$			3.32858i			0.315935i
$112$	2.63447	+	0.244018i	0.248934	+	0.0230576i
$113$	6.54677	−	6.54677i	0.615869	−	0.615869i	−0.328600	−	0.944469i	$-0.606577\pi$
$113$	6.54677	−	6.54677i	0.615869	−	0.615869i	0.944469	+	0.328600i	$0.106577\pi$
$114$	−1.53632	+	0.886994i	−0.143889	+	0.0830746i
$115$		0			0
$116$	−1.92314	+	3.33098i	−0.178559	+	0.309273i
$117$	−3.70732	−	0.993373i	−0.342742	−	0.0918374i
$118$	−7.33099	−	7.33099i	−0.674872	−	0.674872i
$119$	5.51145	+	2.03786i	0.505234	+	0.186811i
$120$		0			0
$121$	3.94052	+	6.82518i	0.358229	+	0.620471i
$122$	1.75710	+	6.55758i	0.159080	+	0.593695i
$123$	3.07978	+	11.4939i	0.277694	+	1.03637i
$124$	5.16471	+	8.94554i	0.463805	+	0.803333i
$125$		0			0
$126$	−2.48155	−	0.917556i	−0.221074	−	0.0817424i
$127$	−12.5444	−	12.5444i	−1.11313	−	1.11313i	−0.992724	−	0.120409i	$-0.961579\pi$
$127$	−12.5444	−	12.5444i	−1.11313	−	1.11313i	−0.120409	−	0.992724i	$-0.538421\pi$
$128$	−0.965926	−	0.258819i	−0.0853766	−	0.0228766i
$129$	2.44896	−	4.24172i	0.215619	−	0.373462i
$130$		0			0
$131$	0.830756	−	0.479637i	0.0725835	−	0.0419061i	−0.463269	−	0.886218i	$-0.653324\pi$
$131$	0.830756	−	0.479637i	0.0725835	−	0.0419061i	0.535853	+	0.844312i	$0.319990\pi$
$132$	1.24879	−	1.24879i	0.108693	−	0.108693i
$133$	4.67353	+	0.432886i	0.405246	+	0.0375359i
$134$		−	7.63862i		−	0.659877i
$135$		0			0
$136$	−1.92342	−	1.11049i	−0.164932	−	0.0952233i
$137$	10.7669	−	2.88499i	0.919880	−	0.246481i	0.232346	−	0.972633i	$-0.425360\pi$
$137$	10.7669	−	2.88499i	0.919880	−	0.246481i	0.687534	+	0.726152i	$0.258693\pi$
$138$	−1.04741	+	3.90900i	−0.0891616	+	0.332756i
$139$	−13.5695			−1.15095			−0.575477	−	0.817818i	$-0.695184\pi$
$139$	−13.5695			−1.15095			−0.575477	+	0.817818i	$0.695184\pi$
$140$		0			0
$141$	6.14785			0.517742
$142$	−2.77435	+	10.3540i	−0.232819	+	0.868891i
$143$	−6.54733	+	1.75435i	−0.547516	+	0.146706i
$144$	0.866025	+	0.500000i	0.0721688	+	0.0416667i
$145$		0			0
$146$			10.6328i			0.879979i
$147$	3.95640	+	5.77468i	0.326318	+	0.476288i
$148$	−2.35366	+	2.35366i	−0.193470	+	0.193470i
$149$	8.74565	−	5.04930i	0.716471	−	0.413655i	−0.0969812	−	0.995286i	$-0.530919\pi$
$149$	8.74565	−	5.04930i	0.716471	−	0.413655i	0.813453	+	0.581631i	$0.197585\pi$
$150$		0			0
$151$	7.15497	−	12.3928i	0.582263	−	1.00851i	−0.412948	−	0.910755i	$-0.635501\pi$
$151$	7.15497	−	12.3928i	0.582263	−	1.00851i	0.995211	−	0.0977541i	$-0.0311659\pi$
$152$	−1.71354	−	0.459142i	−0.138987	−	0.0372413i
$153$	1.57046	+	1.57046i	0.126964	+	0.126964i
$154$	−4.60563	+	0.787924i	−0.371133	+	0.0634927i
$155$		0			0
$156$	−1.91905	−	3.32389i	−0.153647	−	0.266124i
$157$	2.48036	+	9.25683i	0.197954	+	0.738776i	0.991482	+	0.130242i	$0.0415754\pi$
$157$	2.48036	+	9.25683i	0.197954	+	0.738776i	−0.793528	+	0.608534i	$0.791758\pi$
$158$	3.28465	+	12.2585i	0.261313	+	0.975233i
$159$	0.205275	+	0.355547i	0.0162794	+	0.0281967i
$160$		0			0
$161$	8.23705	−	6.84049i	0.649170	−	0.539106i
$162$	−0.707107	−	0.707107i	−0.0555556	−	0.0555556i
$163$	11.4401	+	3.06537i	0.896058	+	0.240098i	0.677323	−	0.735686i	$-0.263140\pi$
$163$	11.4401	+	3.06537i	0.896058	+	0.240098i	0.218736	+	0.975784i	$0.429807\pi$
$164$	−5.94967	+	10.3051i	−0.464591	+	0.804695i
$165$		0			0
$166$	2.37878	−	1.37339i	0.184629	−	0.106596i
$167$	−6.95883	+	6.95883i	−0.538490	+	0.538490i	−0.923085	−	0.384595i	$-0.874341\pi$
$167$	−6.95883	+	6.95883i	−0.538490	+	0.538490i	0.384595	+	0.923085i	$0.374341\pi$
$168$	−1.10591	−	2.40353i	−0.0853229	−	0.185436i
$169$			1.73100i			0.133154i
$170$		0			0
$171$	1.53632	+	0.886994i	0.117485	+	0.0678301i
$172$	4.73102	−	1.26767i	0.360737	−	0.0966592i
$173$	2.24296	−	8.37084i	0.170529	−	0.636423i	−0.826741	−	0.562583i	$-0.809808\pi$
$173$	2.24296	−	8.37084i	0.170529	−	0.636423i	0.997270	−	0.0738403i	$-0.0235255\pi$
$174$	3.84628			0.291586
$175$		0			0
$176$	1.76606			0.133122
$177$	−2.68333	+	10.0143i	−0.201691	+	0.752722i
$178$	−1.07822	+	0.288908i	−0.0808160	+	0.0216546i
$179$	11.5646	+	6.67682i	0.864378	+	0.499049i	0.865476	−	0.500951i	$-0.167016\pi$
$179$	11.5646	+	6.67682i	0.864378	+	0.499049i	−0.00109809	+	0.999999i	$0.500350\pi$
$180$		0			0
$181$		−	8.73922i		−	0.649581i	−0.945786	−	0.324791i	$-0.894706\pi$
$181$		−	8.73922i		−	0.649581i	0.945786	−	0.324791i	$-0.105294\pi$
$182$	−0.936566	+	10.1114i	−0.0694229	+	0.749505i
$183$	4.80048	−	4.80048i	0.354862	−	0.354862i
$184$	−3.50471	+	2.02344i	−0.258371	+	0.149170i
$185$		0			0
$186$	5.16471	−	8.94554i	0.378695	−	0.655919i
$187$	3.78871	+	1.01518i	0.277058	+	0.0742374i
$188$	4.34719	+	4.34719i	0.317051	+	0.317051i
$189$	0.446149	+	2.60786i	0.0324525	+	0.189694i
$190$		0			0
$191$	5.43796	+	9.41883i	0.393477	+	0.681523i	0.992906	−	0.118906i	$-0.0379386\pi$
$191$	5.43796	+	9.41883i	0.393477	+	0.681523i	−0.599428	+	0.800429i	$0.704605\pi$
$192$	0.258819	+	0.965926i	0.0186787	+	0.0697097i
$193$	−2.89908	−	10.8195i	−0.208680	−	0.778806i	−0.988296	−	0.152548i	$-0.951252\pi$
$193$	−2.89908	−	10.8195i	−0.208680	−	0.778806i	0.779616	−	0.626258i	$-0.215414\pi$
$194$	−5.13869	−	8.90047i	−0.368936	−	0.639016i
$195$		0			0
$196$	−1.28572	+	6.88091i	−0.0918371	+	0.491494i
$197$	10.3775	+	10.3775i	0.739367	+	0.739367i	0.972456	−	0.233088i	$-0.0748831\pi$
$197$	10.3775	+	10.3775i	0.739367	+	0.739367i	−0.233088	+	0.972456i	$0.574883\pi$
$198$	−1.70588	−	0.457089i	−0.121232	−	0.0324839i
$199$	−9.28152	+	16.0761i	−0.657949	+	1.13960i	0.323197	+	0.946332i	$0.395243\pi$
$199$	−9.28152	+	16.0761i	−0.657949	+	1.13960i	−0.981146	+	0.193270i	$0.938091\pi$
$200$		0			0
$201$	−6.61524	+	3.81931i	−0.466603	+	0.269394i
$202$	12.9730	−	12.9730i	0.912780	−	0.912780i
$203$	−8.30609	−	5.87928i	−0.582973	−	0.412645i
$204$			2.22097i			0.155499i
$205$		0			0
$206$	7.89804	+	4.55993i	0.550282	+	0.317706i
$207$	3.90900	−	1.04741i	0.271694	−	0.0728002i
$208$	0.993373	−	3.70732i	0.0688780	−	0.257056i
$209$	3.13296			0.216712
$210$		0			0
$211$	−0.453133			−0.0311950			−0.0155975	−	0.999878i	$-0.504965\pi$
$211$	−0.453133			−0.0311950			−0.0155975	+	0.999878i	$0.504965\pi$
$212$	−0.106258	+	0.396561i	−0.00729784	+	0.0272359i
$213$	10.3540	−	2.77435i	0.709446	−	0.190096i
$214$	−12.7779	−	7.37735i	−0.873483	−	0.504305i
$215$		0			0
$216$		−	1.00000i		−	0.0680414i
$217$	−24.8271	+	11.4234i	−1.68537	+	0.775473i
$218$	14.2474	−	14.2474i	0.964955	−	0.964955i
$219$	9.20830	−	5.31641i	0.622239	−	0.359250i
$220$		0			0
$221$	4.26215	−	7.38226i	0.286703	−	0.496585i
$222$	3.21516	+	0.861499i	0.215787	+	0.0578201i
$223$	−4.67260	−	4.67260i	−0.312901	−	0.312901i	0.533132	−	0.846032i	$-0.321015\pi$
$223$	−4.67260	−	4.67260i	−0.312901	−	0.312901i	−0.846032	+	0.533132i	$0.821015\pi$
$224$	0.917556	−	2.48155i	0.0613068	−	0.165806i
$225$		0			0
$226$	−4.62927	−	8.01813i	−0.307934	−	0.533358i
$227$	4.29835	+	16.0416i	0.285291	+	1.06472i	0.948626	+	0.316399i	$0.102474\pi$
$227$	4.29835	+	16.0416i	0.285291	+	1.06472i	−0.663335	+	0.748323i	$0.730860\pi$
$228$	0.459142	+	1.71354i	0.0304074	+	0.113482i
$229$	−6.77075	−	11.7273i	−0.447423	−	0.774960i	0.550794	−	0.834641i	$-0.314325\pi$
$229$	−6.77075	−	11.7273i	−0.447423	−	0.774960i	−0.998217	+	0.0596810i	$0.980992\pi$
$230$		0			0
$231$	2.98518	+	3.59463i	0.196410	+	0.236510i
$232$	2.71973	+	2.71973i	0.178559	+	0.178559i
$233$	11.1838	+	2.99668i	0.732672	+	0.196319i	0.605819	−	0.795603i	$-0.292846\pi$
$233$	11.1838	+	2.99668i	0.732672	+	0.196319i	0.126853	+	0.991922i	$0.459512\pi$
$234$	−1.91905	+	3.32389i	−0.125452	+	0.217290i
$235$		0			0
$236$	−8.97859	+	5.18379i	−0.584456	+	0.337436i
$237$	8.97383	−	8.97383i	0.582913	−	0.582913i
$238$	3.39489	−	4.79621i	0.220058	−	0.310892i
$239$			17.0264i			1.10135i	0.834721	+	0.550673i	$0.185629\pi$
$239$			17.0264i			1.10135i	−0.834721	+	0.550673i	$0.814371\pi$
$240$		0			0
$241$	16.3866	+	9.46081i	1.05555	+	0.609424i	0.924199	−	0.381911i	$-0.124734\pi$
$241$	16.3866	+	9.46081i	1.05555	+	0.609424i	0.131355	+	0.991335i	$0.458067\pi$
$242$	7.61250	−	2.03976i	0.489350	−	0.131121i
$243$	−0.258819	+	0.965926i	−0.0166032	+	0.0619642i
$244$	6.78891			0.434615
$245$		0			0
$246$	11.8993			0.758674
$247$	1.76223	−	6.57674i	0.112128	−	0.418468i
$248$	9.97746	−	2.67345i	0.633569	−	0.169764i
$249$	−2.37878	−	1.37339i	−0.150749	−	0.0870350i
$250$		0			0
$251$		−	18.1527i		−	1.14579i	−0.819629	−	0.572894i	$-0.805821\pi$
$251$		−	18.1527i		−	1.14579i	0.819629	−	0.572894i	$-0.194179\pi$
$252$	−1.52856	+	2.15951i	−0.0962904	+	0.136037i
$253$	5.05372	−	5.05372i	0.317725	−	0.317725i
$254$	−15.3637	+	8.87021i	−0.964002	+	0.556567i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	23.2500	+	6.22983i	1.45030	+	0.388606i	0.896127	−	0.443797i	$-0.146369\pi$
$257$	23.2500	+	6.22983i	1.45030	+	0.388606i	0.554170	+	0.832403i	$0.313036\pi$
$258$	−3.46335	−	3.46335i	−0.215619	−	0.215619i
$259$	−5.62632	−	6.77499i	−0.349603	−	0.420978i
$260$		0			0
$261$	−1.92314	−	3.33098i	−0.119039	−	0.206182i
$262$	−0.248279	−	0.926588i	−0.0153387	−	0.0572448i
$263$	−3.63274	−	13.5576i	−0.224004	−	0.835995i	−0.982801	−	0.184668i	$-0.940879\pi$
$263$	−3.63274	−	13.5576i	−0.224004	−	0.835995i	0.758797	−	0.651328i	$-0.225788\pi$
$264$	−0.883028	−	1.52945i	−0.0543466	−	0.0941311i
$265$		0			0
$266$	1.62773	−	4.40224i	0.0998027	−	0.269919i
$267$	0.789311	+	0.789311i	0.0483051	+	0.0483051i
$268$	−7.37834	−	1.97702i	−0.450704	−	0.120766i
$269$	−13.2762	+	22.9951i	−0.809466	+	1.40204i	0.103768	+	0.994602i	$0.466910\pi$
$269$	−13.2762	+	22.9951i	−0.809466	+	1.40204i	−0.913234	+	0.407435i	$0.866423\pi$
$270$		0			0
$271$	10.3582	−	5.98031i	0.629216	−	0.363278i	−0.151232	−	0.988498i	$-0.548324\pi$
$271$	10.3582	−	5.98031i	0.629216	−	0.363278i	0.780448	+	0.625220i	$0.214991\pi$
$272$	−1.57046	+	1.57046i	−0.0952233	+	0.0952233i
$273$	9.22499	−	4.24460i	0.558322	−	0.256895i
$274$		−	11.1467i		−	0.673399i
$275$		0			0
$276$	3.50471	+	2.02344i	0.210959	+	0.121797i
$277$	−2.28118	+	0.611241i	−0.137063	+	0.0367259i	−0.326698	−	0.945129i	$-0.605936\pi$
$277$	−2.28118	+	0.611241i	−0.137063	+	0.0367259i	0.189635	+	0.981855i	$0.439269\pi$
$278$	−3.51206	+	13.1072i	−0.210639	+	0.786116i
$279$	−10.3294			−0.618406
$280$		0			0
$281$	−11.0306			−0.658033			−0.329017	−	0.944324i	$-0.606717\pi$
$281$	−11.0306			−0.658033			−0.329017	+	0.944324i	$0.606717\pi$
$282$	1.59118	−	5.93837i	0.0947534	−	0.353625i
$283$	−22.6131	+	6.05917i	−1.34421	+	0.360180i	−0.857995	−	0.513658i	$-0.828290\pi$
$283$	−22.6131	+	6.05917i	−1.34421	+	0.360180i	−0.486217	+	0.873838i	$0.661623\pi$
$284$	9.28317	+	5.35964i	0.550855	+	0.318036i
$285$		0			0
$286$			6.77830i			0.400809i
$287$	−25.6968	−	18.1889i	−1.51683	−	1.07366i
$288$	0.707107	−	0.707107i	0.0416667	−	0.0416667i
$289$	10.4506	−	6.03364i	0.614740	−	0.354920i
$290$		0			0
$291$	−5.13869	+	8.90047i	−0.301235	+	0.521755i
$292$	10.2705	+	2.75198i	0.601037	+	0.161047i
$293$	15.4837	+	15.4837i	0.904565	+	0.904565i	0.995827	−	0.0912620i	$-0.0290901\pi$
$293$	15.4837	+	15.4837i	0.904565	+	0.904565i	−0.0912620	+	0.995827i	$0.529090\pi$
$294$	6.60190	−	2.32699i	0.385031	−	0.135713i
$295$		0			0
$296$	1.66429	+	2.88263i	0.0967348	+	0.167550i
$297$	0.457089	+	1.70588i	0.0265230	+	0.0989852i
$298$	−2.61371	−	9.75450i	−0.151408	−	0.565063i
$299$	−7.76618	−	13.4514i	−0.449130	−	0.777916i
$300$		0			0
$301$	2.18520	+	12.7731i	0.125953	+	0.736228i
$302$	−10.1186	−	10.1186i	−0.582263	−	0.582263i
$303$	−17.7215	−	4.74846i	−1.01807	−	0.272792i
$304$	−0.886994	+	1.53632i	−0.0508726	+	0.0881139i
$305$		0			0
$306$	1.92342	−	1.11049i	0.109954	−	0.0634822i
$307$	−2.12149	+	2.12149i	−0.121080	+	0.121080i	−0.765050	−	0.643971i	$-0.777286\pi$
$307$	−2.12149	+	2.12149i	−0.121080	+	0.121080i	0.643971	+	0.765050i	$0.277286\pi$
$308$	−0.430950	+	4.65263i	−0.0245557	+	0.265108i
$309$		−	9.11987i		−	0.518811i
$310$		0			0
$311$	13.0082	+	7.51027i	0.737626	+	0.425868i	0.821205	−	0.570633i	$-0.193302\pi$
$311$	13.0082	+	7.51027i	0.737626	+	0.425868i	−0.0835796	+	0.996501i	$0.526635\pi$
$312$	−3.70732	+	0.993373i	−0.209886	+	0.0562387i
$313$	3.44701	−	12.8644i	0.194836	−	0.727139i	−0.797473	−	0.603355i	$-0.793830\pi$
$313$	3.44701	−	12.8644i	0.194836	−	0.727139i	0.992309	−	0.123784i	$-0.0395031\pi$
$314$	9.58338			0.540821
$315$		0			0
$316$	12.6909			0.713920
$317$	−3.59802	+	13.4280i	−0.202085	+	0.754192i	0.788233	+	0.615377i	$0.210996\pi$
$317$	−3.59802	+	13.4280i	−0.202085	+	0.754192i	−0.990318	+	0.138815i	$0.955671\pi$
$318$	0.396561	−	0.106258i	0.0222380	−	0.00595867i
$319$	−5.88269	−	3.39638i	−0.329368	−	0.190160i
$320$		0			0
$321$			14.7547i			0.823527i
$322$	−4.47550	−	9.72682i	−0.249410	−	0.542055i
$323$	−2.78598	+	2.78598i	−0.155016	+	0.155016i
$324$	−0.866025	+	0.500000i	−0.0481125	+	0.0277778i
$325$		0			0
$326$	5.92183	−	10.2569i	0.327980	−	0.568078i
$327$	−19.4623	−	5.21491i	−1.07627	−	0.288385i
$328$	8.41410	+	8.41410i	0.464591	+	0.464591i
$329$	−12.5133	+	10.3918i	−0.689883	+	0.572916i
$330$		0			0
$331$	9.31631	+	16.1363i	0.512071	+	0.886932i	0.999902	+	0.0139944i	$0.00445470\pi$
$331$	9.31631	+	16.1363i	0.512071	+	0.886932i	−0.487832	+	0.872938i	$0.662212\pi$
$332$	−0.710918	−	2.65318i	−0.0390167	−	0.145612i
$333$	−0.861499	−	3.21516i	−0.0472099	−	0.176190i
$334$	4.92063	+	8.52279i	0.269245	+	0.466346i
$335$		0			0
$336$	−2.60786	+	0.446149i	−0.142271	+	0.0243394i
$337$	−9.63568	−	9.63568i	−0.524889	−	0.524889i	0.394155	−	0.919044i	$-0.371037\pi$
$337$	−9.63568	−	9.63568i	−0.524889	−	0.524889i	−0.919044	+	0.394155i	$0.871037\pi$
$338$	1.67202	+	0.448015i	0.0909456	+	0.0243688i
$339$	−4.62927	+	8.01813i	−0.251427	+	0.435485i
$340$		0			0
$341$	−15.7983	+	9.12117i	−0.855528	+	0.493939i
$342$	1.25440	−	1.25440i	0.0678301	−	0.0678301i
$343$	−17.8138	−	5.06626i	−0.961857	−	0.273552i
$344$		−	4.89791i		−	0.264078i
$345$		0			0
$346$	−7.50509	−	4.33306i	−0.403476	−	0.232947i
$347$	33.6890	−	9.02693i	1.80852	−	0.484591i	0.813264	−	0.581895i	$-0.197689\pi$
$347$	33.6890	−	9.02693i	1.80852	−	0.484591i	0.995255	+	0.0973042i	$0.0310220\pi$
$348$	0.995491	−	3.71522i	0.0533639	−	0.199157i
$349$	−1.49727			−0.0801469			−0.0400735	−	0.999197i	$-0.512759\pi$
$349$	−1.49727			−0.0801469			−0.0400735	+	0.999197i	$0.512759\pi$
$350$		0			0
$351$	3.83810			0.204863
$352$	0.457089	−	1.70588i	0.0243629	−	0.0909237i
$353$	5.76343	−	1.54431i	0.306756	−	0.0821951i	−0.102157	−	0.994768i	$-0.532574\pi$
$353$	5.76343	−	1.54431i	0.306756	−	0.0821951i	0.408913	+	0.912573i	$0.365908\pi$
$354$	8.97859	+	5.18379i	0.477207	+	0.275515i
$355$		0			0
$356$			1.11625i			0.0591614i
$357$	−5.85109	−	0.541957i	−0.309673	−	0.0286834i
$358$	9.44244	−	9.44244i	0.499049	−	0.499049i
$359$	14.9989	−	8.65964i	0.791613	−	0.457038i	−0.0489170	−	0.998803i	$-0.515577\pi$
$359$	14.9989	−	8.65964i	0.791613	−	0.457038i	0.840530	+	0.541765i	$0.182244\pi$
$360$		0			0
$361$	7.92648	−	13.7291i	0.417183	−	0.722583i
$362$	−8.44144	−	2.26188i	−0.443672	−	0.118882i
$363$	−5.57274	−	5.57274i	−0.292493	−	0.292493i
$364$	9.52443	+	3.52167i	0.499216	+	0.184586i
$365$		0			0
$366$	−3.39445	−	5.87936i	−0.177431	−	0.307319i
$367$	−1.41960	−	5.29802i	−0.0741025	−	0.276554i	0.918926	−	0.394430i	$-0.129058\pi$
$367$	−1.41960	−	5.29802i	−0.0741025	−	0.276554i	−0.993028	+	0.117876i	$0.962391\pi$
$368$	1.04741	+	3.90900i	0.0546001	+	0.203770i
$369$	−5.94967	−	10.3051i	−0.309727	−	0.536464i
$370$		0			0
$371$	−1.01880	−	0.376703i	−0.0528935	−	0.0195574i
$372$	−7.30401	−	7.30401i	−0.378695	−	0.378695i
$373$	29.7901	+	7.98224i	1.54247	+	0.413305i	0.927064	−	0.374903i	$-0.122324\pi$
$373$	29.7901	+	7.98224i	1.54247	+	0.413305i	0.615410	+	0.788207i	$0.288991\pi$
$374$	1.96118	−	3.39686i	0.101410	−	0.175648i
$375$		0			0
$376$	5.32419	−	3.07393i	0.274574	−	0.158526i
$377$	−10.4386	+	10.4386i	−0.537615	+	0.537615i
$378$	2.63447	+	0.244018i	0.135503	+	0.0125509i
$379$			12.9203i			0.663670i	0.943337	+	0.331835i	$0.107668\pi$
$379$			12.9203i			0.663670i	−0.943337	+	0.331835i	$0.892332\pi$
$380$		0			0
$381$	15.3637	+	8.87021i	0.787104	+	0.454435i
$382$	10.5053	−	2.81490i	0.537500	−	0.144023i
$383$	0.308002	−	1.14948i	0.0157382	−	0.0587356i	−0.957610	−	0.288067i	$-0.906987\pi$
$383$	0.308002	−	1.14948i	0.0157382	−	0.0587356i	0.973348	+	0.229332i	$0.0736540\pi$
$384$	1.00000			0.0510310
$385$		0			0
$386$	−11.2012			−0.570126
$387$	−1.26767	+	4.73102i	−0.0644394	+	0.240491i
$388$	−9.92718	+	2.65998i	−0.503976	+	0.135040i
$389$	−8.25213	−	4.76437i	−0.418400	−	0.241563i	0.275993	−	0.961160i	$-0.410993\pi$
$389$	−8.25213	−	4.76437i	−0.418400	−	0.241563i	−0.694392	+	0.719597i	$0.744327\pi$
$390$		0			0
$391$			8.98802i			0.454544i
$392$	6.31368	+	3.02282i	0.318889	+	0.152675i
$393$	−0.678310	+	0.678310i	−0.0342162	+	0.0342162i
$394$	12.7098	−	7.33801i	0.640311	−	0.369684i
$395$		0			0
$396$	−0.883028	+	1.52945i	−0.0443738	+	0.0768578i
$397$	27.5610	+	7.38494i	1.38324	+	0.370639i	0.872299	−	0.488974i	$-0.162629\pi$
$397$	27.5610	+	7.38494i	1.38324	+	0.370639i	0.510946	+	0.859613i	$0.329295\pi$
$398$	13.1260	+	13.1260i	0.657949	+	0.657949i
$399$	−4.62632	+	0.791463i	−0.231606	+	0.0396227i
$400$		0			0
$401$	−19.6150	−	33.9741i	−0.979526	−	1.69659i	−0.664111	−	0.747634i	$-0.731190\pi$
$401$	−19.6150	−	33.9741i	−0.979526	−	1.69659i	−0.315415	−	0.948954i	$-0.602144\pi$
$402$	1.97702	+	7.37834i	0.0986049	+	0.367998i
$403$	10.2610	+	38.2945i	0.511135	+	1.90758i
$404$	−9.17333	−	15.8887i	−0.456390	−	0.790491i
$405$		0			0
$406$	−7.82873	+	6.50140i	−0.388533	+	0.322659i
$407$	−4.15670	−	4.15670i	−0.206040	−	0.206040i
$408$	2.14529	+	0.574830i	0.106208	+	0.0284583i
$409$	4.32912	−	7.49826i	0.214061	−	0.370765i	−0.738920	−	0.673793i	$-0.764664\pi$
$409$	4.32912	−	7.49826i	0.214061	−	0.370765i	0.952982	+	0.303028i	$0.0979974\pi$
$410$		0			0
$411$	−9.65336	+	5.57337i	−0.476165	+	0.274914i
$412$	6.44872	−	6.44872i	0.317706	−	0.317706i
$413$	−11.4656	−	24.9188i	−0.564187	−	1.22617i
$414$		−	4.04689i		−	0.198894i
$415$		0			0
$416$	−3.32389	−	1.91905i	−0.162967	−	0.0940891i
$417$	13.1072	−	3.51206i	0.641861	−	0.171986i
$418$	0.810871	−	3.02621i	0.0396610	−	0.148017i
$419$	4.29623			0.209884			0.104942	−	0.994478i	$-0.466534\pi$
$419$	4.29623			0.209884			0.104942	+	0.994478i	$0.466534\pi$
$420$		0			0
$421$	−18.8346			−0.917945			−0.458972	−	0.888451i	$-0.651782\pi$
$421$	−18.8346			−0.917945			−0.458972	+	0.888451i	$0.651782\pi$
$422$	−0.117279	+	0.437693i	−0.00570907	+	0.0213066i
$423$	−5.93837	+	1.59118i	−0.288733	+	0.0773659i
$424$	0.355547	+	0.205275i	0.0172669	+	0.00996904i
$425$		0			0
$426$		−	10.7193i		−	0.519351i
$427$	−1.65662	+	17.8852i	−0.0801693	+	0.865525i
$428$	−10.4332	+	10.4332i	−0.504305	+	0.504305i
$429$	5.87018	−	3.38915i	0.283415	−	0.163630i
$430$		0			0
$431$	−3.46231	+	5.99690i	−0.166774	+	0.288860i	−0.937284	−	0.348567i	$-0.886668\pi$
$431$	−3.46231	+	5.99690i	−0.166774	+	0.288860i	0.770510	+	0.637428i	$0.220002\pi$
$432$	−0.965926	−	0.258819i	−0.0464731	−	0.0124524i
$433$	−11.5154	−	11.5154i	−0.553393	−	0.553393i	0.374025	−	0.927419i	$-0.377977\pi$
$433$	−11.5154	−	11.5154i	−0.553393	−	0.553393i	−0.927419	+	0.374025i	$0.877977\pi$
$434$	4.60846	+	26.9377i	0.221213	+	1.29305i
$435$		0			0
$436$	−10.0744	−	17.4494i	−0.482477	−	0.835675i
$437$	1.85810	+	6.93451i	0.0888848	+	0.331723i
$438$	−2.75198	−	10.2705i	−0.131495	−	0.490745i
$439$	9.11194	+	15.7823i	0.434889	+	0.753250i	0.997287	−	0.0736169i	$-0.0234542\pi$
$439$	9.11194	+	15.7823i	0.434889	+	0.753250i	−0.562397	+	0.826867i	$0.690121\pi$
$440$		0			0
$441$	−5.31618	−	4.55392i	−0.253152	−	0.216853i
$442$	−6.02759	−	6.02759i	−0.286703	−	0.286703i
$443$	−31.7136	−	8.49765i	−1.50676	−	0.403735i	−0.591403	−	0.806376i	$-0.701426\pi$
$443$	−31.7136	−	8.49765i	−1.50676	−	0.403735i	−0.915358	+	0.402641i	$0.868092\pi$
$444$	1.66429	−	2.88263i	0.0789837	−	0.136804i
$445$		0			0
$446$	−5.72275	+	3.30403i	−0.270980	+	0.156450i
$447$	−7.14079	+	7.14079i	−0.337748	+	0.337748i
$448$	−2.15951	−	1.52856i	−0.102027	−	0.0722178i
$449$			8.14032i			0.384165i	0.981379	+	0.192083i	$0.0615242\pi$
$449$			8.14032i			0.384165i	−0.981379	+	0.192083i	$0.938476\pi$
$450$		0			0
$451$	−18.1994	−	10.5075i	−0.856978	−	0.494777i
$452$	−8.94306	+	2.39629i	−0.420646	+	0.112712i
$453$	−3.70368	+	13.8223i	−0.174014	+	0.649430i
$454$	16.6075			0.779430
$455$		0			0
$456$	1.77399			0.0830746
$457$	−1.18177	+	4.41041i	−0.0552806	+	0.206310i	−0.988042	−	0.154184i	$-0.950725\pi$
$457$	−1.18177	+	4.41041i	−0.0552806	+	0.206310i	0.932762	+	0.360494i	$0.117392\pi$
$458$	−13.0801	+	3.50480i	−0.611192	+	0.163768i
$459$	−1.92342	−	1.11049i	−0.0897774	−	0.0518330i
$460$		0			0
$461$			7.54894i			0.351589i	0.984427	+	0.175795i	$0.0562495\pi$
$461$			7.54894i			0.351589i	−0.984427	+	0.175795i	$0.943751\pi$
$462$	4.24477	−	1.95310i	0.197485	−	0.0908665i
$463$	8.87647	−	8.87647i	0.412525	−	0.412525i	−0.470092	−	0.882617i	$-0.655779\pi$
$463$	8.87647	−	8.87647i	0.412525	−	0.412525i	0.882617	+	0.470092i	$0.155779\pi$
$464$	3.33098	−	1.92314i	0.154637	−	0.0892796i
$465$		0			0
$466$	5.78914	−	10.0271i	0.268177	−	0.464495i
$467$	−11.1162	−	2.97858i	−0.514397	−	0.137832i	−0.00772331	−	0.999970i	$-0.502458\pi$
$467$	−11.1162	−	2.97858i	−0.514397	−	0.137832i	−0.506674	+	0.862138i	$0.669125\pi$
$468$	2.71395	+	2.71395i	0.125452	+	0.125452i
$469$	7.00886	−	18.9556i	0.323639	−	0.875290i
$470$		0			0
$471$	−4.79169	−	8.29945i	−0.220789	−	0.382418i
$472$	2.68333	+	10.0143i	0.123510	+	0.460946i
$473$	2.23878	+	8.35525i	0.102939	+	0.384175i
$474$	−6.34546	−	10.9907i	−0.291457	−	0.504817i
$475$		0			0
$476$	−3.75412	−	4.52057i	−0.172070	−	0.207200i
$477$	−0.290303	−	0.290303i	−0.0132921	−	0.0132921i
$478$	16.4462	+	4.40676i	0.752233	+	0.201560i
$479$	6.17379	−	10.6933i	0.282088	−	0.488590i	−0.689811	−	0.723989i	$-0.742306\pi$
$479$	6.17379	−	10.6933i	0.282088	−	0.488590i	0.971899	+	0.235399i	$0.0756398\pi$
$480$		0			0
$481$	−11.0638	+	6.38770i	−0.504467	+	0.291254i
$482$	13.3796	−	13.3796i	0.609424	−	0.609424i
$483$	−6.18593	+	8.73931i	−0.281469	+	0.397652i
$484$		−	7.88104i		−	0.358229i
$485$		0			0
$486$	0.866025	+	0.500000i	0.0392837	+	0.0226805i
$487$	−15.0556	+	4.03414i	−0.682235	+	0.182804i	−0.583260	−	0.812286i	$-0.698223\pi$
$487$	−15.0556	+	4.03414i	−0.682235	+	0.182804i	−0.0989752	+	0.995090i	$0.531556\pi$
$488$	1.75710	−	6.55758i	0.0795401	−	0.296848i
$489$	−11.8437			−0.535589
$490$		0			0
$491$	−2.67474			−0.120709			−0.0603547	−	0.998177i	$-0.519223\pi$
$491$	−2.67474			−0.120709			−0.0603547	+	0.998177i	$0.519223\pi$
$492$	3.07978	−	11.4939i	0.138847	−	0.518184i
$493$	8.25140	−	2.21096i	0.371624	−	0.0995764i
$494$	−5.89654	−	3.40437i	−0.265298	−	0.153170i
$495$		0			0
$496$		−	10.3294i		−	0.463805i
$497$	−16.3851	+	23.1484i	−0.734972	+	1.03835i
$498$	−1.94227	+	1.94227i	−0.0870350	+	0.0870350i
$499$	−15.7413	+	9.08825i	−0.704678	+	0.406846i	−0.809087	−	0.587688i	$-0.800038\pi$
$499$	−15.7413	+	9.08825i	−0.704678	+	0.406846i	0.104410	+	0.994534i	$0.466705\pi$
$500$		0			0
$501$	4.92063	−	8.52279i	0.219838	−	0.380770i
$502$	−17.5342	−	4.69827i	−0.782588	−	0.209694i
$503$	3.59630	+	3.59630i	0.160351	+	0.160351i	0.782722	−	0.622371i	$-0.213831\pi$
$503$	3.59630	+	3.59630i	0.160351	+	0.160351i	−0.622371	+	0.782722i	$0.713831\pi$
$504$	1.69031	+	2.03540i	0.0752923	+	0.0906640i
$505$		0			0
$506$	−3.57352	−	6.18952i	−0.158862	−	0.275158i
$507$	−0.448015	−	1.67202i	−0.0198971	−	0.0742568i
$508$	4.59156	+	17.1359i	0.203718	+	0.760284i
$509$	2.40629	+	4.16782i	0.106657	+	0.184735i	0.914414	−	0.404780i	$-0.132652\pi$
$509$	2.40629	+	4.16782i	0.106657	+	0.184735i	−0.807757	+	0.589516i	$0.799319\pi$
$510$		0			0
$511$	−9.75621	+	26.3859i	−0.431589	+	1.16724i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	−1.71354	−	0.459142i	−0.0756547	−	0.0202716i
$514$	12.0351	−	20.8454i	0.530846	−	0.919452i
$515$		0			0
$516$	−4.24172	+	2.44896i	−0.186731	+	0.107809i
$517$	−7.67738	+	7.67738i	−0.337651	+	0.337651i
$518$	−8.00034	+	3.68111i	−0.351515	+	0.161739i
$519$			8.66613i			0.380401i
$520$		0			0
$521$	4.61481	+	2.66436i	0.202178	+	0.116728i	0.597671	−	0.801741i	$-0.296093\pi$
$521$	4.61481	+	2.66436i	0.202178	+	0.116728i	−0.395493	+	0.918469i	$0.629426\pi$
$522$	−3.71522	+	0.995491i	−0.162611	+	0.0435714i
$523$	−1.58561	+	5.91757i	−0.0693338	+	0.258757i	−0.991889	−	0.127108i	$-0.959430\pi$
$523$	−1.58561	+	5.91757i	−0.0693338	+	0.258757i	0.922555	+	0.385866i	$0.126097\pi$
$524$	−0.959275			−0.0419061
$525$		0			0
$526$	−14.0358			−0.611991
$527$	5.93766	−	22.1596i	0.258648	−	0.965289i
$528$	−1.70588	+	0.457089i	−0.0742389	+	0.0198923i
$529$	−5.73541	−	3.31134i	−0.249366	−	0.143971i
$530$		0			0
$531$		−	10.3676i		−	0.449915i
$532$	−3.83095	−	2.71165i	−0.166093	−	0.117565i
$533$	−32.2942	+	32.2942i	−1.39881	+	1.39881i
$534$	0.966705	−	0.558127i	0.0418334	−	0.0241525i
$535$		0			0
$536$	−3.81931	+	6.61524i	−0.164969	+	0.285735i
$537$	−12.8986	−	3.45617i	−0.556617	−	0.149145i
$538$	18.7754	+	18.7754i	0.809466	+	0.809466i
$539$	−12.1521	−	2.27065i	−0.523427	−	0.0978040i
$540$		0			0
$541$	6.81239	+	11.7994i	0.292887	+	0.507296i	0.974491	−	0.224426i	$-0.0720506\pi$
$541$	6.81239	+	11.7994i	0.292887	+	0.507296i	−0.681604	+	0.731721i	$0.738717\pi$
$542$	−3.09564	−	11.5531i	−0.132969	−	0.496247i
$543$	2.26188	+	8.44144i	0.0970664	+	0.362257i
$544$	1.11049	+	1.92342i	0.0476117	+	0.0824658i
$545$		0			0
$546$	−1.71236	−	10.0092i	−0.0732823	−	0.428356i
$547$	14.8290	+	14.8290i	0.634042	+	0.634042i	0.949079	−	0.315037i	$-0.102017\pi$
$547$	14.8290	+	14.8290i	0.634042	+	0.634042i	−0.315037	+	0.949079i	$0.602017\pi$
$548$	−10.7669	−	2.88499i	−0.459940	−	0.123241i
$549$	−3.39445	+	5.87936i	−0.144872	+	0.250925i
$550$		0			0
$551$	5.90911	−	3.41163i	0.251737	−	0.145340i
$552$	2.86158	−	2.86158i	0.121797	−	0.121797i
$553$	−3.09681	+	33.4339i	−0.131690	+	1.42175i
$554$			2.36165i			0.100337i
$555$		0			0
$556$	11.7516	+	6.78477i	0.498378	+	0.287738i
$557$	0.0387479	−	0.0103825i	0.00164180	−	0.000439920i	−0.257998	−	0.966145i	$-0.583063\pi$
$557$	0.0387479	−	0.0103825i	0.00164180	−	0.000439920i	0.259640	+	0.965706i	$0.416396\pi$
$558$	−2.67345	+	9.97746i	−0.113176	+	0.422379i
$559$	18.7987			0.795099
$560$		0			0
$561$	−3.92236			−0.165602
$562$	−2.85494	+	10.6548i	−0.120428	+	0.449445i
$563$	−13.4327	+	3.59929i	−0.566122	+	0.151692i	−0.530518	−	0.847674i	$-0.678002\pi$
$563$	−13.4327	+	3.59929i	−0.566122	+	0.151692i	−0.0356047	+	0.999366i	$0.511336\pi$
$564$	−5.32419	−	3.07393i	−0.224189	−	0.129436i
$565$		0			0
$566$			23.4108i			0.984031i
$567$	−1.10591	−	2.40353i	−0.0464439	−	0.100939i
$568$	7.57968	−	7.57968i	0.318036	−	0.318036i
$569$	17.1817	−	9.91984i	0.720293	−	0.415861i	−0.0945677	−	0.995518i	$-0.530147\pi$
$569$	17.1817	−	9.91984i	0.720293	−	0.415861i	0.814860	+	0.579657i	$0.196814\pi$
$570$		0			0
$571$	2.94454	−	5.10010i	0.123225	−	0.213432i	−0.797813	−	0.602906i	$-0.794010\pi$
$571$	2.94454	−	5.10010i	0.123225	−	0.213432i	0.921038	+	0.389473i	$0.127343\pi$
$572$	6.54733	+	1.75435i	0.273758	+	0.0733532i
$573$	−7.69044	−	7.69044i	−0.321273	−	0.321273i
$574$	−24.2199	+	20.1135i	−1.01092	+	0.839523i
$575$		0			0
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$	−3.85984	−	14.4051i	−0.160687	−	0.599692i	−0.998551	−	0.0538132i	$-0.982862\pi$
$577$	−3.85984	−	14.4051i	−0.160687	−	0.599692i	0.837864	−	0.545879i	$-0.183804\pi$
$578$	−3.12324	−	11.6561i	−0.129910	−	0.484830i
$579$	5.60060	+	9.70052i	0.232753	+	0.403140i
$580$		0			0
$581$	7.16322	−	1.22547i	0.297180	−	0.0508411i
$582$	7.26720	+	7.26720i	0.301235	+	0.301235i
$583$	−0.700349	−	0.187658i	−0.0290055	−	0.00777200i
$584$	5.31641	−	9.20830i	0.219995	−	0.381042i
$585$		0			0
$586$	18.9635	−	10.9486i	0.783376	−	0.452282i
$587$	4.86057	−	4.86057i	0.200617	−	0.200617i	−0.599647	−	0.800264i	$-0.704692\pi$
$587$	4.86057	−	4.86057i	0.200617	−	0.200617i	0.800264	+	0.599647i	$0.204692\pi$
$588$	−0.539001	−	6.97922i	−0.0222280	−	0.287818i
$589$		−	18.3243i		−	0.755039i
$590$		0			0
$591$	−12.7098	−	7.33801i	−0.522812	−	0.301846i
$592$	3.21516	−	0.861499i	0.132142	−	0.0354074i
$593$	5.48532	−	20.4715i	0.225255	−	0.840664i	−0.757047	−	0.653361i	$-0.773359\pi$
$593$	5.48532	−	20.4715i	0.225255	−	0.840664i	0.982302	−	0.187304i	$-0.0599748\pi$
$594$	1.76606			0.0724622
$595$		0			0
$596$	−10.0986			−0.413655
$597$	4.80447	−	17.9305i	0.196634	−	0.733847i
$598$	−15.0031	+	4.02007i	−0.613523	+	0.164393i
$599$	10.0409	+	5.79712i	0.410260	+	0.236864i	0.690902	−	0.722949i	$-0.257214\pi$
$599$	10.0409	+	5.79712i	0.410260	+	0.236864i	−0.280641	+	0.959813i	$0.590547\pi$
$600$		0			0
$601$		−	15.3561i		−	0.626387i	−0.949689	−	0.313193i	$-0.898601\pi$
$601$		−	15.3561i		−	0.626387i	0.949689	−	0.313193i	$-0.101399\pi$
$602$	12.9034	+	1.19518i	0.525904	+	0.0487119i
$603$	5.40132	−	5.40132i	0.219959	−	0.219959i
$604$	−12.3928	+	7.15497i	−0.504254	+	0.291131i
$605$		0			0
$606$	−9.17333	+	15.8887i	−0.372641	+	0.645433i
$607$	−21.7853	−	5.83734i	−0.884237	−	0.236931i	−0.212003	−	0.977269i	$-0.567999\pi$
$607$	−21.7853	−	5.83734i	−0.884237	−	0.236931i	−0.672234	+	0.740339i	$0.734665\pi$
$608$	1.25440	+	1.25440i	0.0508726	+	0.0508726i
$609$	9.54474	+	3.52918i	0.386772	+	0.143009i
$610$		0			0
$611$	11.7980	+	20.4348i	0.477297	+	0.826703i
$612$	−0.574830	−	2.14529i	−0.0232361	−	0.0867183i
$613$	1.23846	+	4.62200i	0.0500209	+	0.186681i	0.986416	−	0.164267i	$-0.0525260\pi$
$613$	1.23846	+	4.62200i	0.0500209	+	0.186681i	−0.936395	+	0.350948i	$0.885859\pi$
$614$	1.50012	+	2.59828i	0.0605399	+	0.104858i
$615$		0			0
$616$	4.38256	+	1.62046i	0.176578	+	0.0652900i
$617$	−17.3498	−	17.3498i	−0.698475	−	0.698475i	0.265606	−	0.964082i	$-0.414428\pi$
$617$	−17.3498	−	17.3498i	−0.698475	−	0.698475i	−0.964082	+	0.265606i	$0.914428\pi$
$618$	−8.80911	−	2.36040i	−0.354355	−	0.0949490i
$619$	10.4801	−	18.1521i	0.421232	−	0.729596i	−0.574828	−	0.818274i	$-0.694931\pi$
$619$	10.4801	−	18.1521i	0.421232	−	0.729596i	0.996060	+	0.0886786i	$0.0282644\pi$
$620$		0			0
$621$	−3.50471	+	2.02344i	−0.140639	+	0.0811980i
$622$	10.6211	−	10.6211i	0.425868	−	0.425868i
$623$	−2.94074	−	0.272387i	−0.117818	−	0.0109129i
$624$			3.83810i			0.153647i
$625$		0			0
$626$	−11.5339	−	6.65911i	−0.460988	−	0.266152i
$627$	−3.02621	+	0.810871i	−0.120855	+	0.0323831i
$628$	2.48036	−	9.25683i	0.0989772	−	0.369388i
$629$	7.39267			0.294765
$630$		0			0
$631$	−48.7823			−1.94199			−0.970996	−	0.239095i	$-0.923149\pi$
$631$	−48.7823			−1.94199			−0.970996	+	0.239095i	$0.923149\pi$
$632$	3.28465	−	12.2585i	0.130656	−	0.487616i
$633$	0.437693	−	0.117279i	0.0173967	−	0.00466144i
$634$	12.0392	+	6.95084i	0.478138	+	0.276053i
$635$		0			0
$636$		−	0.410550i		−	0.0162794i
$637$	−11.6019	+	24.2325i	−0.459683	+	0.960128i
$638$	−4.80320	+	4.80320i	−0.190160	+	0.190160i
$639$	−9.28317	+	5.35964i	−0.367237	+	0.212024i
$640$		0			0
$641$	−6.03196	+	10.4477i	−0.238248	+	0.412658i	−0.960212	−	0.279273i	$-0.909906\pi$
$641$	−6.03196	+	10.4477i	−0.238248	+	0.412658i	0.721964	+	0.691931i	$0.243240\pi$
$642$	14.2519	+	3.81880i	0.562480	+	0.150716i
$643$	−15.5935	−	15.5935i	−0.614947	−	0.614947i	0.329284	−	0.944231i	$-0.393193\pi$
$643$	−15.5935	−	15.5935i	−0.614947	−	0.614947i	−0.944231	+	0.329284i	$0.893193\pi$
$644$	−10.5537	+	1.80551i	−0.415875	+	0.0711472i
$645$		0			0
$646$	1.96999	+	3.41212i	0.0775082	+	0.134248i
$647$	1.69672	+	6.33226i	0.0667051	+	0.248947i	0.991225	−	0.132188i	$-0.0422001\pi$
$647$	1.69672	+	6.33226i	0.0667051	+	0.248947i	−0.924520	+	0.381135i	$0.875533\pi$
$648$	0.258819	+	0.965926i	0.0101674	+	0.0379452i
$649$	−9.15487	−	15.8567i	−0.359360	−	0.622430i
$650$		0			0
$651$	21.0245	−	17.4599i	0.824016	−	0.684308i
$652$	−8.37474	−	8.37474i	−0.327980	−	0.327980i
$653$	−22.3037	−	5.97625i	−0.872811	−	0.233869i	−0.205508	−	0.978655i	$-0.565885\pi$
$653$	−22.3037	−	5.97625i	−0.872811	−	0.233869i	−0.667303	+	0.744787i	$0.732551\pi$
$654$	−10.0744	+	17.4494i	−0.393941	+	0.682326i
$655$		0			0
$656$	10.3051	−	5.94967i	0.402348	−	0.232296i
$657$	−7.51854	+	7.51854i	−0.293326	+	0.293326i
$658$	6.79898	+	14.7765i	0.265052	+	0.576050i
$659$			8.89429i			0.346472i	0.984880	+	0.173236i	$0.0554224\pi$
$659$			8.89429i			0.346472i	−0.984880	+	0.173236i	$0.944578\pi$
$660$		0			0
$661$	7.24046	+	4.18028i	0.281621	+	0.162594i	0.634157	−	0.773204i	$-0.281347\pi$
$661$	7.24046	+	4.18028i	0.281621	+	0.162594i	−0.352536	+	0.935798i	$0.614681\pi$
$662$	17.9977	−	4.82248i	0.699501	−	0.187431i
$663$	−2.20625	+	8.23385i	−0.0856837	+	0.319776i
$664$	−2.74678			−0.106596
$665$		0			0
$666$	−3.32858			−0.128980
$667$	4.02864	−	15.0351i	0.155990	−	0.582161i
$668$	9.50594	−	2.54711i	0.367796	−	0.0985506i
$669$	5.72275	+	3.30403i	0.221254	+	0.127741i
$670$		0			0
$671$			11.9896i			0.462853i
$672$	−0.244018	+	2.63447i	−0.00941321	+	0.101627i
$673$	11.1305	−	11.1305i	0.429048	−	0.429048i	−0.459256	−	0.888304i	$-0.651884\pi$
$673$	11.1305	−	11.1305i	0.429048	−	0.429048i	0.888304	+	0.459256i	$0.151884\pi$
$674$	−11.8013	+	6.81346i	−0.454567	+	0.262444i
$675$		0			0
$676$	0.865499	−	1.49909i	0.0332884	−	0.0576572i
$677$	−41.9335	−	11.2360i	−1.61163	−	0.431836i	−0.663106	−	0.748526i	$-0.730762\pi$
$677$	−41.9335	−	11.2360i	−1.61163	−	0.431836i	−0.948529	+	0.316690i	$0.897429\pi$
$678$	6.54677	+	6.54677i	0.251427	+	0.251427i
$679$	−4.58524	−	26.8020i	−0.175965	−	1.02857i
$680$		0			0
$681$	−8.30377	−	14.3825i	−0.318201	−	0.551140i
$682$	4.72147	+	17.6208i	0.180794	+	0.674734i
$683$	4.62860	+	17.2742i	0.177108	+	0.660977i	0.996183	+	0.0872904i	$0.0278208\pi$
$683$	4.62860	+	17.2742i	0.177108	+	0.660977i	−0.819075	+	0.573687i	$0.805513\pi$
$684$	−0.886994	−	1.53632i	−0.0339151	−	0.0587426i
$685$		0			0
$686$	−9.50420	+	15.8956i	−0.362872	+	0.606897i
$687$	9.57528	+	9.57528i	0.365320	+	0.365320i
$688$	−4.73102	−	1.26767i	−0.180368	−	0.0483296i
$689$	−0.787866	+	1.36462i	−0.0300153	+	0.0519880i
$690$		0			0
$691$	30.5564	−	17.6417i	1.16242	−	0.671123i	0.210537	−	0.977586i	$-0.432479\pi$
$691$	30.5564	−	17.6417i	1.16242	−	0.671123i	0.951883	+	0.306463i	$0.0991456\pi$
$692$	−6.12788	+	6.12788i	−0.232947	+	0.232947i
$693$	−3.81382	−	2.69953i	−0.144875	−	0.102547i
$694$		−	34.8774i		−	1.32393i
$695$		0			0
$696$	−3.33098	−	1.92314i	−0.126260	−	0.0728964i
$697$	25.5276	−	6.84009i	0.966926	−	0.259087i
$698$	−0.387522	+	1.44625i	−0.0146679	+	0.0547414i
$699$	−11.5783			−0.437930
$700$		0			0
$701$	−14.9862			−0.566020			−0.283010	−	0.959117i	$-0.591333\pi$
$701$	−14.9862			−0.566020			−0.283010	+	0.959117i	$0.591333\pi$
$702$	0.993373	−	3.70732i	0.0374924	−	0.139924i
$703$	5.70366	−	1.52829i	0.215117	−	0.0576405i
$704$	−1.52945	−	0.883028i	−0.0576433	−	0.0332804i
$705$		0			0
$706$		−	5.96674i		−	0.224561i
$707$	44.0968	−	20.2898i	1.65843	−	0.763075i
$708$	7.33099	−	7.33099i	0.275515	−	0.275515i
$709$	7.19605	−	4.15464i	0.270253	−	0.156031i	−0.358750	−	0.933434i	$-0.616797\pi$
$709$	7.19605	−	4.15464i	0.270253	−	0.156031i	0.629003	+	0.777403i	$0.283463\pi$
$710$		0			0
$711$	−6.34546	+	10.9907i	−0.237973	+	0.412182i
$712$	1.07822	+	0.288908i	0.0404080	+	0.0108273i
$713$	−29.5585	−	29.5585i	−1.10697	−	1.10697i
$714$	−2.03786	+	5.51145i	−0.0762652	+	0.206261i
$715$		0			0
$716$	−6.67682	−	11.5646i	−0.249524	−	0.432189i
$717$	−4.40676	−	16.4462i	−0.164573	−	0.614196i
$718$	−4.48256	−	16.7291i	−0.167288	−	0.624326i
$719$	7.07678	+	12.2574i	0.263920	+	0.457122i	0.967280	−	0.253711i	$-0.0816513\pi$
$719$	7.07678	+	12.2574i	0.263920	+	0.457122i	−0.703360	+	0.710833i	$0.748318\pi$
$720$		0			0
$721$	15.4154	+	18.5626i	0.574099	+	0.691307i
$722$	−11.2097	−	11.2097i	−0.417183	−	0.417183i
$723$	−18.2769	−	4.89728i	−0.679725	−	0.182132i
$724$	−4.36961	+	7.56839i	−0.162395	+	0.281277i
$725$		0			0
$726$	−6.82518	+	3.94052i	−0.253306	+	0.146246i
$727$	−19.9622	+	19.9622i	−0.740357	+	0.740357i	−0.972647	−	0.232290i	$-0.925378\pi$
$727$	−19.9622	+	19.9622i	−0.740357	+	0.740357i	0.232290	+	0.972647i	$0.425378\pi$
$728$	5.86678	−	8.28842i	0.217437	−	0.307189i
$729$		−	1.00000i		−	0.0370370i
$730$		0			0
$731$	−9.42073	−	5.43906i	−0.348438	−	0.201171i
$732$	−6.55758	+	1.75710i	−0.242375	+	0.0649442i
$733$	12.0119	−	44.8290i	0.443670	−	1.65580i	−0.275755	−	0.961228i	$-0.588928\pi$
$733$	12.0119	−	44.8290i	0.443670	−	1.65580i	0.719425	−	0.694570i	$-0.244405\pi$
$734$	−5.48491			−0.202452
$735$		0			0
$736$	4.04689			0.149170
$737$	3.49153	−	13.0306i	0.128612	−	0.479987i
$738$	−11.4939	+	3.07978i	−0.423095	+	0.113368i
$739$	15.1424	+	8.74246i	0.557022	+	0.321597i	0.751949	−	0.659221i	$-0.229114\pi$
$739$	15.1424	+	8.74246i	0.557022	+	0.321597i	−0.194927	+	0.980818i	$0.562447\pi$
$740$		0			0
$741$			6.80874i			0.250125i
$742$	−0.627552	+	0.886588i	−0.0230382	+	0.0325477i
$743$	12.2427	−	12.2427i	0.449143	−	0.449143i	−0.445927	−	0.895069i	$-0.647126\pi$
$743$	12.2427	−	12.2427i	0.449143	−	0.449143i	0.895069	+	0.445927i	$0.147126\pi$
$744$	−8.94554	+	5.16471i	−0.327960	+	0.189348i
$745$		0			0
$746$	15.4205	−	26.7091i	0.564585	−	0.977889i
$747$	2.65318	+	0.710918i	0.0970749	+	0.0260111i
$748$	−2.77353	−	2.77353i	−0.101410	−	0.101410i
$749$	−24.9400	−	30.0317i	−0.911287	−	1.09734i
$750$		0			0
$751$	12.4732	+	21.6042i	0.455154	+	0.788350i	0.998697	−	0.0510312i	$-0.0162508\pi$
$751$	12.4732	+	21.6042i	0.455154	+	0.788350i	−0.543543	+	0.839381i	$0.682917\pi$
$752$	−1.59118	−	5.93837i	−0.0580244	−	0.216550i
$753$	4.69827	+	17.5342i	0.171214	+	0.638981i
$754$	7.38120	+	12.7846i	0.268808	+	0.465588i
$755$		0			0
$756$	0.917556	−	2.48155i	0.0333712	−	0.0902531i
$757$	32.4637	+	32.4637i	1.17991	+	1.17991i	0.979765	+	0.200149i	$0.0641427\pi$
$757$	32.4637	+	32.4637i	1.17991	+	1.17991i	0.200149	+	0.979765i	$0.435857\pi$
$758$	12.4800	+	3.34401i	0.453295	+	0.121460i
$759$	−3.57352	+	6.18952i	−0.129711	+	0.224665i
$760$		0			0
$761$	28.5750	−	16.4978i	1.03584	−	0.598045i	0.117191	−	0.993109i	$-0.462611\pi$
$761$	28.5750	−	16.4978i	1.03584	−	0.598045i	0.918653	+	0.395065i	$0.129278\pi$
$762$	12.5444	−	12.5444i	0.454435	−	0.454435i
$763$	48.4284	−	22.2828i	1.75322	−	0.806693i
$764$		−	10.8759i		−	0.393477i
$765$		0			0
$766$	−1.03059	−	0.595014i	−0.0372369	−	0.0214987i
$767$	−38.4359	+	10.2989i	−1.38784	+	0.371871i
$768$	0.258819	−	0.965926i	0.00933933	−	0.0348548i
$769$	10.0980			0.364144			0.182072	−	0.983285i	$-0.441720\pi$
$769$	10.0980			0.364144			0.182072	+	0.983285i	$0.441720\pi$
$770$		0			0
$771$	−24.0702			−0.866867
$772$	−2.89908	+	10.8195i	−0.104340	+	0.389403i
$773$	11.4236	−	3.06094i	0.410878	−	0.110094i	−0.0474585	−	0.998873i	$-0.515112\pi$
$773$	11.4236	−	3.06094i	0.410878	−	0.110094i	0.458336	+	0.888779i	$0.348446\pi$
$774$	4.24172	+	2.44896i	0.152465	+	0.0880259i
$775$		0			0
$776$			10.2774i			0.368936i
$777$	7.18811	+	5.08794i	0.257872	+	0.182529i
$778$	−6.73784	+	6.73784i	−0.241563	+	0.241563i
$779$	18.2812	−	10.5546i	0.654991	−	0.378159i
$780$		0			0
$781$	−9.46543	+	16.3946i	−0.338700	+	0.586645i
$782$	8.68176	+	2.32627i	0.310459	+	0.0831873i
$783$	2.71973	+	2.71973i	0.0971953	+	0.0971953i
$784$	4.55392	−	5.31618i	0.162640	−	0.189864i
$785$		0			0
$786$	0.479637	+	0.830756i	0.0171081	+	0.0296321i
$787$	2.27001	+	8.47179i	0.0809171	+	0.301987i	0.994510	−	0.104644i	$-0.0333703\pi$
$787$	2.27001	+	8.47179i	0.0809171	+	0.301987i	−0.913593	+	0.406631i	$0.866704\pi$
$788$	−3.79843	−	14.1760i	−0.135314	−	0.504997i
$789$	7.01791	+	12.1554i	0.249844	+	0.432743i
$790$		0			0
$791$	−4.13068	−	24.1450i	−0.146870	−	0.858497i
$792$	1.24879	+	1.24879i	0.0443738	+	0.0443738i
$793$	25.1686	+	6.74391i	0.893764	+	0.239483i
$794$	14.2666	−	24.7105i	0.506303	−	0.876942i
$795$		0			0
$796$	16.0761	−	9.28152i	0.569801	−	0.328975i
$797$	26.4972	−	26.4972i	0.938580	−	0.938580i	−0.0596400	−	0.998220i	$-0.518995\pi$
$797$	26.4972	−	26.4972i	0.938580	−	0.938580i	0.998220	+	0.0596400i	$0.0189953\pi$
$798$	−0.432886	+	4.67353i	−0.0153240	+	0.165441i
$799$		−	13.6542i		−	0.483051i
$800$		0			0
$801$	−0.966705	−	0.558127i	−0.0341568	−	0.0197205i
$802$	−37.8932	+	10.1535i	−1.33806	+	0.358531i
$803$	−4.86015	+	18.1383i	−0.171511	+	0.640088i
$804$	7.63862			0.269394
$805$		0			0
$806$	39.6453			1.39645
$807$	6.87229	−	25.6477i	0.241916	−	0.902842i
$808$	−17.7215	+	4.74846i	−0.623441	+	0.167050i
$809$	−34.0232	−	19.6433i	−1.19619	−	0.690622i	−0.236489	−	0.971634i	$-0.575997\pi$
$809$	−34.0232	−	19.6433i	−1.19619	−	0.690622i	−0.959704	+	0.281012i	$0.909330\pi$
$810$		0			0
$811$		−	9.61165i		−	0.337511i	−0.985658	−	0.168755i	$-0.946025\pi$
$811$		−	9.61165i		−	0.337511i	0.985658	−	0.168755i	$-0.0539748\pi$
$812$	4.25364	+	9.24465i	0.149274	+	0.324424i
$813$	−8.45744	+	8.45744i	−0.296615	+	0.296615i
$814$	−5.09089	+	2.93923i	−0.178436	+	0.103020i
$815$		0			0
$816$	1.11049	−	1.92342i	0.0388748	−	0.0673331i
$817$	−8.39277	−	2.24884i	−0.293626	−	0.0786769i
$818$	−6.12230	−	6.12230i	−0.214061	−	0.214061i
$819$	−7.81207	+	6.48757i	−0.272976	+	0.226694i
$820$		0			0
$821$	−25.9357	−	44.9219i	−0.905162	−	1.56779i	−0.820700	−	0.571359i	$-0.806416\pi$
$821$	−25.9357	−	44.9219i	−0.905162	−	1.56779i	−0.0844618	−	0.996427i	$-0.526917\pi$
$822$	2.88499	+	10.7669i	0.100626	+	0.375540i
$823$	−2.69263	−	10.0490i	−0.0938592	−	0.350287i	0.902985	−	0.429672i	$-0.141371\pi$
$823$	−2.69263	−	10.0490i	−0.0938592	−	0.350287i	−0.996844	+	0.0793852i	$0.974704\pi$
$824$	−4.55993	−	7.89804i	−0.158853	−	0.275141i
$825$		0			0
$826$	−27.0372	+	4.62548i	−0.940746	+	0.160941i
$827$	−7.55951	−	7.55951i	−0.262870	−	0.262870i	0.563349	−	0.826219i	$-0.309513\pi$
$827$	−7.55951	−	7.55951i	−0.262870	−	0.262870i	−0.826219	+	0.563349i	$0.809513\pi$
$828$	−3.90900	−	1.04741i	−0.135847	−	0.0364001i
$829$	16.1525	−	27.9770i	0.561001	−	0.971682i	−0.436409	−	0.899748i	$-0.643750\pi$
$829$	16.1525	−	27.9770i	0.561001	−	0.971682i	0.997409	−	0.0719331i	$-0.0229168\pi$
$830$		0			0
$831$	2.04525	−	1.18083i	0.0709490	−	0.0409624i
$832$	−2.71395	+	2.71395i	−0.0940891	+	0.0940891i
$833$	12.8254	−	8.78704i	0.444374	−	0.304453i
$834$		−	13.5695i		−	0.469875i
$835$		0			0
$836$	−2.71323	−	1.56648i	−0.0938389	−	0.0541779i
$837$	9.97746	−	2.67345i	0.344871	−	0.0924080i
$838$	1.11195	−	4.14984i	0.0384115	−	0.143354i
$839$	−24.7218			−0.853490			−0.426745	−	0.904372i	$-0.640340\pi$
$839$	−24.7218			−0.853490			−0.426745	+	0.904372i	$0.640340\pi$
$840$		0			0
$841$	14.2061			0.489866
$842$	−4.87477	+	18.1929i	−0.167996	+	0.626968i
$843$	10.6548	−	2.85494i	0.366970	−	0.0983294i
$844$	0.392425	+	0.226566i	0.0135078	+	0.00779874i
$845$		0			0
$846$			6.14785i			0.211367i
$847$	20.7624	+	1.92312i	0.713405	+	0.0660791i
$848$	0.290303	−	0.290303i	0.00996904	−	0.00996904i
$849$	20.2744	−	11.7054i	0.695815	−	0.401729i
$850$		0			0
$851$	6.73519	−	11.6657i	0.230879	−	0.399895i
$852$	−10.3540	−	2.77435i	−0.354723	−	0.0950478i
$853$	28.0435	+	28.0435i	0.960191	+	0.960191i	0.999237	−	0.0390463i	$-0.0124320\pi$
$853$	28.0435	+	28.0435i	0.960191	+	0.960191i	−0.0390463	+	0.999237i	$0.512432\pi$
$854$	16.8470	+	6.22920i	0.576493	+	0.213159i
$855$		0			0
$856$	7.37735	+	12.7779i	0.252153	+	0.436741i
$857$	12.3144	+	45.9579i	0.420652	+	1.56989i	0.773239	+	0.634115i	$0.218635\pi$
$857$	12.3144	+	45.9579i	0.420652	+	1.56989i	−0.352587	+	0.935779i	$0.614698\pi$
$858$	−1.75435	−	6.54733i	−0.0598926	−	0.223522i
$859$	26.8560	+	46.5160i	0.916315	+	1.58710i	0.804964	+	0.593324i	$0.202185\pi$
$859$	26.8560	+	46.5160i	0.916315	+	1.58710i	0.111351	+	0.993781i	$0.464482\pi$
$860$		0			0
$861$	29.5288	+	10.9183i	1.00634	+	0.372095i
$862$	4.89645	+	4.89645i	0.166774	+	0.166774i
$863$	38.6139	+	10.3466i	1.31443	+	0.352201i	0.846890	−	0.531768i	$-0.178472\pi$
$863$	38.6139	+	10.3466i	1.31443	+	0.352201i	0.467544	+	0.883970i	$0.345139\pi$
$864$	−0.500000	+	0.866025i	−0.0170103	+	0.0294628i
$865$		0			0
$866$	−14.1034	+	8.14260i	−0.479253	+	0.276697i
$867$	−8.53286	+	8.53286i	−0.289791	+	0.289791i
$868$	27.2126	+	2.52057i	0.923656	+	0.0855536i
$869$			22.4129i			0.760305i
$870$		0			0
$871$	−25.3900	−	14.6589i	−0.860306	−	0.496698i
$872$	−19.4623	+	5.21491i	−0.659076	+	0.176599i
$873$	2.65998	−	9.92718i	0.0900267	−	0.335984i
$874$	7.17914			0.242838
$875$		0			0
$876$	−10.6328			−0.359250
$877$	1.96884	−	7.34780i	0.0664829	−	0.248118i	−0.924685	−	0.380734i	$-0.875671\pi$
$877$	1.96884	−	7.34780i	0.0664829	−	0.248118i	0.991167	+	0.132617i	$0.0423379\pi$
$878$	17.6029	−	4.71669i	0.594070	−	0.159180i
$879$	−18.9635	−	10.9486i	−0.639624	−	0.369287i
$880$		0			0
$881$			37.1659i			1.25215i	0.779763	+	0.626075i	$0.215340\pi$
$881$			37.1659i			1.25215i	−0.779763	+	0.626075i	$0.784660\pi$
$882$	−5.77468	+	3.95640i	−0.194444	+	0.133219i
$883$	−25.7803	+	25.7803i	−0.867577	+	0.867577i	−0.992204	−	0.124627i	$-0.960227\pi$
$883$	−25.7803	+	25.7803i	−0.867577	+	0.867577i	0.124627	+	0.992204i	$0.460227\pi$
$884$	−7.38226	+	4.26215i	−0.248292	+	0.143352i
$885$		0			0
$886$	−16.4162	+	28.4337i	−0.551513	+	0.955248i
$887$	14.4006	+	3.85864i	0.483526	+	0.129560i	0.492344	−	0.870401i	$-0.336140\pi$
$887$	14.4006	+	3.85864i	0.483526	+	0.129560i	−0.00881809	+	0.999961i	$0.502807\pi$
$888$	−2.35366	−	2.35366i	−0.0789837	−	0.0789837i
$889$	−46.2646	+	7.91487i	−1.55167	+	0.265456i
$890$		0			0
$891$	−0.883028	−	1.52945i	−0.0295826	−	0.0512385i
$892$	1.71029	+	6.38289i	0.0572648	+	0.213715i
$893$	−2.82274	−	10.5346i	−0.0944593	−	0.352527i
$894$	5.04930	+	8.74565i	0.168874	+	0.292498i
$895$		0			0
$896$	−2.03540	+	1.69031i	−0.0679980	+	0.0564692i
$897$	10.9830	+	10.9830i	0.366713	+	0.366713i
$898$	7.86295	+	2.10687i	0.262390	+	0.0703072i
$899$	−19.8649	+	34.4071i	−0.662533	+	1.14754i
$900$		0			0
$901$	0.789659	−	0.455910i	0.0263074	−	0.0151886i
$902$	−14.8598	+	14.8598i	−0.494777	+	0.494777i
$903$	−5.41666	−	11.7723i	−0.180255	−	0.391757i
$904$			9.25854i			0.307934i
$905$		0			0
$906$	12.3928	+	7.15497i	0.411722	+	0.237708i
$907$	20.7799	−	5.56795i	0.689984	−	0.184881i	0.103244	−	0.994656i	$-0.467078\pi$
$907$	20.7799	−	5.56795i	0.689984	−	0.184881i	0.586740	+	0.809775i	$0.300411\pi$
$908$	4.29835	−	16.0416i	0.142646	−	0.532361i
$909$	18.3467			0.608520
$910$		0			0
$911$	23.6120			0.782301			0.391151	−	0.920327i	$-0.372077\pi$
$911$	23.6120			0.782301			0.391151	+	0.920327i	$0.372077\pi$
$912$	0.459142	−	1.71354i	0.0152037	−	0.0567410i
$913$	4.68567	−	1.25552i	0.155073	−	0.0415517i
$914$	3.95426	+	2.28300i	0.130795	+	0.0755148i
$915$		0			0
$916$			13.5415i			0.447423i
$917$	0.234081	−	2.52719i	0.00773002	−	0.0834550i
$918$	−1.57046	+	1.57046i	−0.0518330	+	0.0518330i
$919$	−38.2901	+	22.1068i	−1.26307	+	0.729236i	−0.973668	−	0.227971i	$-0.926791\pi$
$919$	−38.2901	+	22.1068i	−1.26307	+	0.729236i	−0.289406	+	0.957207i	$0.593458\pi$
$920$		0			0
$921$	1.50012	−	2.59828i	0.0494306	−	0.0856163i
$922$	7.29172	+	1.95381i	0.240140	+	0.0643453i
$923$	29.0915	+	29.0915i	0.957560	+	0.957560i
$924$	−0.787924	−	4.60563i	−0.0259208	−	0.151514i
$925$		0			0
$926$	−6.27661	−	10.8714i	−0.206262	−	0.357257i
$927$	2.36040	+	8.80911i	0.0775255	+	0.289329i
$928$	−0.995491	−	3.71522i	−0.0326786	−	0.121958i
$929$	−0.388224	−	0.672424i	−0.0127372	−	0.0220615i	0.859587	−	0.510990i	$-0.170721\pi$
$929$	−0.388224	−	0.672424i	−0.0127372	−	0.0220615i	−0.872324	+	0.488929i	$0.837388\pi$
$930$		0			0
$931$	8.07860	−	9.43085i	0.264766	−	0.309084i
$932$	−8.18707	−	8.18707i	−0.268177	−	0.268177i
$933$	−14.5087	−	3.88760i	−0.474995	−	0.127274i
$934$	−5.75418	+	9.96652i	−0.188282	+	0.326115i
$935$		0			0
$936$	3.32389	−	1.91905i	0.108645	−	0.0627261i
$937$	−0.494892	+	0.494892i	−0.0161674	+	0.0161674i	−0.715144	−	0.698977i	$-0.753639\pi$
$937$	−0.494892	+	0.494892i	−0.0161674	+	0.0161674i	0.698977	+	0.715144i	$0.253639\pi$
$938$	−16.4957	−	11.6761i	−0.538604	−	0.381239i
$939$			13.3182i			0.434624i
$940$		0			0
$941$	15.9777	+	9.22471i	0.520857	+	0.300717i	0.737285	−	0.675582i	$-0.236107\pi$
$941$	15.9777	+	9.22471i	0.520857	+	0.300717i	−0.216428	+	0.976299i	$0.569441\pi$
$942$	−9.25683	+	2.48036i	−0.301604	+	0.0808145i
$943$	12.4635	−	46.5145i	0.405868	−	1.51472i
$944$	10.3676			0.337436
$945$		0			0
$946$	8.64999			0.281235
$947$	2.67536	−	9.98459i	0.0869376	−	0.324456i	−0.908736	−	0.417370i	$-0.862952\pi$
$947$	2.67536	−	9.98459i	0.0869376	−	0.324456i	0.995674	+	0.0929149i	$0.0296184\pi$
$948$	−12.2585	+	3.28465i	−0.398137	+	0.106680i
$949$	35.3424	+	20.4049i	1.14726	+	0.662372i
$950$		0			0
$951$		−	13.9017i		−	0.450793i
$952$	−5.33817	+	2.45620i	−0.173011	+	0.0796058i
$953$	−11.1833	+	11.1833i	−0.362263	+	0.362263i	−0.864645	−	0.502383i	$-0.832457\pi$
$953$	−11.1833	+	11.1833i	−0.362263	+	0.362263i	0.502383	+	0.864645i	$0.332457\pi$
$954$	−0.355547	+	0.205275i	−0.0115113	+	0.00664603i
$955$		0			0
$956$	8.51320	−	14.7453i	0.275336	−	0.476897i
$957$	6.56129	+	1.75809i	0.212096	+	0.0568311i
$958$	−8.73106	−	8.73106i	−0.282088	−	0.282088i
$959$	10.2278	−	27.6612i	0.330271	−	0.893227i
$960$		0			0
$961$	37.8485	+	65.5555i	1.22092	+	2.11469i
$962$	3.30652	+	12.3401i	0.106606	+	0.397861i
$963$	−3.81880	−	14.2519i	−0.123059	−	0.459263i
$964$	−9.46081	−	16.3866i	−0.304712	−	0.527777i
$965$		0			0
$966$	6.84049	+	8.23705i	0.220089	+	0.265023i
$967$	3.47333	+	3.47333i	0.111695	+	0.111695i	0.760745	−	0.649051i	$-0.224834\pi$
$967$	3.47333	+	3.47333i	0.111695	+	0.111695i	−0.649051	+	0.760745i	$0.724834\pi$
$968$	−7.61250	−	2.03976i	−0.244675	−	0.0655605i
$969$	1.96999	−	3.41212i	0.0632851	−	0.109613i
$970$		0			0
$971$	31.5326	−	18.2054i	1.01193	−	0.584238i	0.100174	−	0.994970i	$-0.468060\pi$
$971$	31.5326	−	18.2054i	1.01193	−	0.584238i	0.911756	+	0.410732i	$0.134727\pi$
$972$	0.707107	−	0.707107i	0.0226805	−	0.0226805i
$973$	−20.7419	+	29.3036i	−0.664955	+	0.939430i
$974$			15.5867i			0.499431i
$975$		0			0
$976$	−5.87936	−	3.39445i	−0.188194	−	0.108654i
$977$	−23.2951	+	6.24191i	−0.745278	+	0.199697i	−0.611422	−	0.791304i	$-0.709402\pi$
$977$	−23.2951	+	6.24191i	−0.745278	+	0.199697i	−0.133855	+	0.991001i	$0.542736\pi$
$978$	−3.06537	+	11.4401i	−0.0980196	+	0.365814i
$979$	−1.97137			−0.0630052
$980$		0			0
$981$	20.1488			0.643303
$982$	−0.692274	+	2.58360i	−0.0220913	+	0.0824460i
$983$	24.7118	−	6.62151i	0.788184	−	0.211193i	0.157794	−	0.987472i	$-0.449562\pi$
$983$	24.7118	−	6.62151i	0.788184	−	0.211193i	0.630390	+	0.776279i	$0.282895\pi$
$984$	−10.3051	−	5.94967i	−0.328516	−	0.189669i
$985$		0			0
$986$		−	8.54248i		−	0.272048i
$987$	9.39738	−	13.2764i	0.299122	−	0.422591i
$988$	−4.81451	+	4.81451i	−0.153170	+	0.153170i
$989$	−17.1658	+	9.91066i	−0.545839	+	0.315141i
$990$		0			0
$991$	−13.1174	+	22.7201i	−0.416689	+	0.721726i	−0.995604	−	0.0936614i	$-0.970143\pi$
$991$	−13.1174	+	22.7201i	−0.416689	+	0.721726i	0.578915	+	0.815388i	$0.303476\pi$
$992$	−9.97746	−	2.67345i	−0.316785	−	0.0848822i
$993$	−13.1752	−	13.1752i	−0.418104	−	0.418104i
$994$	18.1189	+	21.8180i	0.574696	+	0.692026i
$995$		0			0
$996$	1.37339	+	2.37878i	0.0435175	+	0.0753745i
$997$	−9.65822	−	36.0450i	−0.305879	−	1.14156i	−0.932186	−	0.361980i	$-0.882101\pi$
$997$	−9.65822	−	36.0450i	−0.305879	−	1.14156i	0.626307	−	0.779577i	$-0.284566\pi$
$998$	4.70442	+	17.5571i	0.148916	+	0.555762i
$999$	1.66429	+	2.88263i	0.0526558	+	0.0912025i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1050.2.bc.g.157.4		16
5.2	odd	4		210.2.u.a.73.3	✓	16
5.3	odd	4		1050.2.bc.h.493.1		16
5.4	even	2		210.2.u.b.157.2	yes	16
7.5	odd	6		1050.2.bc.h.607.1		16
15.2	even	4		630.2.bv.a.73.2		16
15.14	odd	2		630.2.bv.b.577.3		16
35.4	even	6		1470.2.m.e.97.2		16
35.12	even	12		210.2.u.b.103.2	yes	16
35.17	even	12		1470.2.m.e.1273.2		16
35.19	odd	6		210.2.u.a.187.3	yes	16
35.24	odd	6		1470.2.m.d.97.3		16
35.32	odd	12		1470.2.m.d.1273.3		16
35.33	even	12	inner	1050.2.bc.g.943.4		16
105.47	odd	12		630.2.bv.b.523.3		16
105.89	even	6		630.2.bv.a.397.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.2.u.a.73.3	✓	16	5.2	odd	4
210.2.u.a.187.3	yes	16	35.19	odd	6
210.2.u.b.103.2	yes	16	35.12	even	12
210.2.u.b.157.2	yes	16	5.4	even	2
630.2.bv.a.73.2		16	15.2	even	4
630.2.bv.a.397.2		16	105.89	even	6
630.2.bv.b.523.3		16	105.47	odd	12
630.2.bv.b.577.3		16	15.14	odd	2
1050.2.bc.g.157.4		16	1.1	even	1	trivial
1050.2.bc.g.943.4		16	35.33	even	12	inner
1050.2.bc.h.493.1		16	5.3	odd	4
1050.2.bc.h.607.1		16	7.5	odd	6
1470.2.m.d.97.3		16	35.24	odd	6
1470.2.m.d.1273.3		16	35.32	odd	12
1470.2.m.e.97.2		16	35.4	even	6
1470.2.m.e.1273.2		16	35.17	even	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1050.bc (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.258819 - 0.965926i) q^{2} +(-0.965926 + 0.258819i) q^{3} +(-0.866025 - 0.500000i) q^{4} +1.00000i q^{6} +(1.52856 - 2.15951i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(0.866025 - 0.500000i) q^{9} +O(q^{10})\)	\(q+(0.258819 - 0.965926i) q^{2} +(-0.965926 + 0.258819i) q^{3} +(-0.866025 - 0.500000i) q^{4} +1.00000i q^{6} +(1.52856 - 2.15951i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(0.866025 - 0.500000i) q^{9} +(0.883028 - 1.52945i) q^{11} +(0.965926 + 0.258819i) q^{12} +(-2.71395 - 2.71395i) q^{13} +(-1.69031 - 2.03540i) q^{14} +(0.500000 + 0.866025i) q^{16} +(0.574830 + 2.14529i) q^{17} +(-0.258819 - 0.965926i) q^{18} +(0.886994 + 1.53632i) q^{19} +(-0.917556 + 2.48155i) q^{21} +(-1.24879 - 1.24879i) q^{22} +(3.90900 + 1.04741i) q^{23} +(0.500000 - 0.866025i) q^{24} +(-3.32389 + 1.91905i) q^{26} +(-0.707107 + 0.707107i) q^{27} +(-2.40353 + 1.10591i) q^{28} -3.84628i q^{29} +(-8.94554 - 5.16471i) q^{31} +(0.965926 - 0.258819i) q^{32} +(-0.457089 + 1.70588i) q^{33} +2.22097 q^{34} -1.00000 q^{36} +(0.861499 - 3.21516i) q^{37} +(1.71354 - 0.459142i) q^{38} +(3.32389 + 1.91905i) q^{39} -11.8993i q^{41} +(2.15951 + 1.52856i) q^{42} +(-3.46335 + 3.46335i) q^{43} +(-1.52945 + 0.883028i) q^{44} +(2.02344 - 3.50471i) q^{46} +(-5.93837 - 1.59118i) q^{47} +(-0.707107 - 0.707107i) q^{48} +(-2.32699 - 6.60190i) q^{49} +(-1.11049 - 1.92342i) q^{51} +(0.993373 + 3.70732i) q^{52} +(-0.106258 - 0.396561i) q^{53} +(0.500000 + 0.866025i) q^{54} +(0.446149 + 2.60786i) q^{56} +(-1.25440 - 1.25440i) q^{57} +(-3.71522 - 0.995491i) q^{58} +(5.18379 - 8.97859i) q^{59} +(-5.87936 + 3.39445i) q^{61} +(-7.30401 + 7.30401i) q^{62} +(0.244018 - 2.63447i) q^{63} -1.00000i q^{64} +(1.52945 + 0.883028i) q^{66} +(7.37834 - 1.97702i) q^{67} +(0.574830 - 2.14529i) q^{68} -4.04689 q^{69} -10.7193 q^{71} +(-0.258819 + 0.965926i) q^{72} +(-10.2705 + 2.75198i) q^{73} +(-2.88263 - 1.66429i) q^{74} -1.77399i q^{76} +(-1.95310 - 4.24477i) q^{77} +(2.71395 - 2.71395i) q^{78} +(-10.9907 + 6.34546i) q^{79} +(0.500000 - 0.866025i) q^{81} +(-11.4939 - 3.07978i) q^{82} +(1.94227 + 1.94227i) q^{83} +(2.03540 - 1.69031i) q^{84} +(2.44896 + 4.24172i) q^{86} +(0.995491 + 3.71522i) q^{87} +(0.457089 + 1.70588i) q^{88} +(-0.558127 - 0.966705i) q^{89} +(-10.0092 + 1.71236i) q^{91} +(-2.86158 - 2.86158i) q^{92} +(9.97746 + 2.67345i) q^{93} +(-3.07393 + 5.32419i) q^{94} +(-0.866025 + 0.500000i) q^{96} +(7.26720 - 7.26720i) q^{97} +(-6.97922 + 0.539001i) q^{98} -1.76606i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{7}+O(q^{10}) \) 16 * q + 4 * q^7	\( 16 q + 4 q^{7} + 4 q^{11} - 16 q^{13} - 16 q^{14} + 8 q^{16} - 12 q^{17} + 8 q^{19} + 8 q^{21} - 4 q^{22} + 40 q^{23} + 8 q^{24} - 12 q^{26} + 4 q^{28} - 24 q^{31} - 4 q^{33} - 16 q^{34} - 16 q^{36} + 8 q^{37} + 20 q^{38} + 12 q^{39} - 8 q^{42} + 24 q^{43} - 4 q^{46} - 52 q^{49} + 8 q^{51} - 8 q^{52} + 28 q^{53} + 8 q^{54} + 8 q^{56} + 8 q^{57} + 12 q^{58} - 8 q^{59} + 24 q^{61} + 8 q^{62} + 4 q^{63} + 84 q^{67} - 12 q^{68} + 8 q^{69} - 32 q^{71} - 16 q^{73} + 24 q^{74} - 44 q^{77} + 16 q^{78} - 12 q^{79} + 8 q^{81} - 36 q^{82} - 16 q^{83} - 4 q^{84} - 8 q^{86} - 48 q^{87} + 4 q^{88} + 16 q^{89} + 8 q^{91} - 8 q^{92} + 32 q^{93} - 8 q^{94} + 44 q^{97} - 24 q^{98}+O(q^{100}) \) 16 * q + 4 * q^7 + 4 * q^11 - 16 * q^13 - 16 * q^14 + 8 * q^16 - 12 * q^17 + 8 * q^19 + 8 * q^21 - 4 * q^22 + 40 * q^23 + 8 * q^24 - 12 * q^26 + 4 * q^28 - 24 * q^31 - 4 * q^33 - 16 * q^34 - 16 * q^36 + 8 * q^37 + 20 * q^38 + 12 * q^39 - 8 * q^42 + 24 * q^43 - 4 * q^46 - 52 * q^49 + 8 * q^51 - 8 * q^52 + 28 * q^53 + 8 * q^54 + 8 * q^56 + 8 * q^57 + 12 * q^58 - 8 * q^59 + 24 * q^61 + 8 * q^62 + 4 * q^63 + 84 * q^67 - 12 * q^68 + 8 * q^69 - 32 * q^71 - 16 * q^73 + 24 * q^74 - 44 * q^77 + 16 * q^78 - 12 * q^79 + 8 * q^81 - 36 * q^82 - 16 * q^83 - 4 * q^84 - 8 * q^86 - 48 * q^87 + 4 * q^88 + 16 * q^89 + 8 * q^91 - 8 * q^92 + 32 * q^93 - 8 * q^94 + 44 * q^97 - 24 * q^98

Introduction

L-functions

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